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  • Relationship between Weber function 2 and Struve function 2
    ...f{E}_2$ denotes a [[Weber function]] and $\mathbf{H}_2$ denotes a [[Struve function]].
    223 bytes (31 words) - 04:11, 6 June 2016
  • Modified Struve function
    where $\mathbf{H}_{\nu}$ denotes a [[Struve function]].
    341 bytes (47 words) - 18:32, 24 May 2016
  • Jacobi theta 1
    Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_1$ function is defined by where $\sin$ denotes the [[sine]] function.
    1 KB (176 words) - 20:23, 25 June 2017
  • Relationship between Struve function and hypergeometric pFq
    ...a [[Struve function]], $\pi$ denotes [[pi]], $\Gamma$ denotes the [[gamma function]], and ${}_2F_1$ denotes the [[hypergeometric pFq]].
    443 bytes (55 words) - 13:18, 25 June 2016
  • Lower incomplete gamma
    The lower incomplete gamma function is defined for $\mathrm{Re}(a)>0$ by A single-valued analytic function of $a$ and $x$ can be defined as
    430 bytes (64 words) - 18:32, 24 May 2016
  • Fibonacci numbers
    [[Fibonacci zeta function]]<br /> ...ence|The Fibonacci Zeta Function|1976|Maruti Ram Murty|next=Fibonacci zeta function}}
    2 KB (362 words) - 13:12, 1 August 2018
  • Inverse error function
    The inverse error function is the [[inverse function]] of the [[error function]]. We denote it by writing $\mathrm{erf}^{-1}$. [[Derivative of inverse error function]]<br />
    496 bytes (68 words) - 04:56, 16 September 2016
  • Integral of log of inverse erf from 0 to 1
    where $\mathrm{erf}^{-1}$ denotes the [[inverse error function]], $\log$ denotes the [[logarithm]], and $\gamma$ denotes the [[Euler-Masch
    363 bytes (43 words) - 01:54, 1 July 2017
  • Integral of inverse erf from 0 to 1
    where $\mathrm{erf}^{-1}$ denotes the [[inverse error function]] and $\pi$ denotes [[pi]].
    284 bytes (36 words) - 04:46, 16 September 2016
  • Antiderivative of inverse error function
    where $\mathrm{erf}^{-1}$ denotes the [[inverse error function]], $\exp$ denotes the [[exponential]], and $\pi$ denotes [[pi]].
    369 bytes (50 words) - 03:48, 3 October 2016
  • Dickman–de Bruijn function
    The Dickman–de Bruijn function $\rho(u)$ solves the [[initial value problem]]
    305 bytes (46 words) - 18:31, 24 May 2016
  • Buchstab function
    The Buchstab function is a [[continuous]] function $\omega \colon [1,\infty) \rightarrow (0,\infty)$ defined by the [[initial
    453 bytes (67 words) - 18:31, 24 May 2016
  • Incomplete beta function
    The incomplete beta function is defined by
    319 bytes (42 words) - 01:56, 23 December 2016
  • Relationship between incomplete beta and hypergeometric 2F1
    where $B_x$ denotes the [[incomplete beta function]] and ${}_2F_1$ denotes the [[hypergeometric pFq]].
    264 bytes (38 words) - 20:26, 5 July 2016
  • Fibonacci zeta function
    The Fibonacci zeta function is defined by * {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci numbers|next=Binet's formula}}
    704 bytes (99 words) - 00:25, 24 May 2017
  • Functions named after Peter Gustav Lejeune Dirichlet
    *[[Dirichlet L-function]]
    64 bytes (6 words) - 19:33, 25 July 2015
  • Riemann Siegel theta function
    The Riemann Siegel $\vartheta$ function is defined for $t \in \mathbb{R}$ by where $\log$ denotes the [[logarithm]] and $\Gamma$ denotes the [[gamma function]].
    548 bytes (76 words) - 18:33, 24 May 2016
  • Error function is odd
    ...thrm{erf}$ denotes the [[error function]] (i.e. $\mathrm{erf}$ is an [[odd function]]).
    800 bytes (116 words) - 03:41, 28 March 2017
  • Erfc
    The complementary error function $\mathrm{erfc}$ is defined by the formula where $\mathrm{erf}$ denotes the [[error function]].
    542 bytes (68 words) - 21:56, 6 July 2016
  • Identity
    Let $X$ be any set. The function $\mathrm{id} \colon X \rightarrow X$ defined by $\mathrm{id}(x)=x$ is calle
    390 bytes (58 words) - 23:02, 25 December 2016
  • Reciprocal Fibonacci constant
    [[Fibonacci zeta function]]<br />
    582 bytes (75 words) - 03:40, 25 June 2017
  • Derivative of the exponential function
    where $e^z$ denotes the [[exponential function]].
    806 bytes (115 words) - 00:10, 23 December 2016
  • Faddeeva function
    The Faddeeva function (also called the Kramp function) is defined by ...e [[error function]] and $\mathrm{erfc}$ denotes the [[complementary error function]].
    478 bytes (66 words) - 18:31, 24 May 2016
  • Taylor series of the exponential function
    where $e^z$ is the [[exponential function]].
    255 bytes (35 words) - 04:03, 3 October 2016
  • Bessel-Clifford
    The Bessel-Clifford function $\mathcal{C}_n$ is defined by where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma]] function.
    559 bytes (71 words) - 16:03, 29 April 2017
  • Floor
    The floor function $\mathrm{floor} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes writte
    457 bytes (70 words) - 00:41, 23 December 2016
  • Ceiling
    The ceiling function $\mathrm{ceil} \colon \mathbb{R} \rightarrow \mathbb{Z}$ (sometimes written
    887 bytes (129 words) - 12:44, 14 July 2023
  • Falling factorial
    where $\Gamma$ denotes the [[gamma function]].
    380 bytes (54 words) - 12:27, 11 August 2016
  • Book:Thomas Ernst/A Comprehensive Treatment of q-Calculus
    ::2.16 Weierstraß, formal power series and the $\Gamma$ function :::3.7.1 The $\Gamma$ function
    11 KB (1,149 words) - 15:21, 18 December 2023
  • Value of Ai(0)
    ...m{Ai}$ denotes the [[Airy Ai]] function and $\Gamma$ denotes the [[gamma]] function.
    306 bytes (34 words) - 23:06, 9 June 2016
  • Value of Ai'(0)
    ...m{Ai}$ denotes the [[Airy Ai]] function and $\Gamma$ denotes the [[gamma]] function.
    287 bytes (35 words) - 23:06, 9 June 2016
  • Porter's constant
    ...he [[Euler-Mascheroni constant]], and $\zeta$ denotes the [[Riemann zeta]] function.
    338 bytes (43 words) - 19:00, 24 May 2016
  • Norton's constant
    ...[[logarithm]], $\pi$ denotes [[pi]], $\zeta$ denotes the [[Riemann zeta]] function, and $C$ denotes [[Porter's constant]].
    316 bytes (40 words) - 19:00, 24 May 2016
  • Sierpiński constant
    ...otes the [[Euler-Mascheroni constant]], and $\Gamma$ denotes the [[gamma]] function.
    327 bytes (42 words) - 19:00, 24 May 2016
  • Relationship between sine, imaginary number, logarithm, and the golden ratio
    where $\sin$ denotes the [[sine]] function, $i$ denotes the [[imaginary number]], $\log$ denotes the [[logarithm]], an
    467 bytes (60 words) - 23:31, 27 June 2016
  • Derivative of arctan
    where $\mathrm{arctan}$ denotes the [[arctan|inverse tangent]] function.
    720 bytes (99 words) - 13:05, 22 September 2016
  • Value of Anger at 0
    where $\textbf{J}_{\nu}$ denotes an [[Anger function]], $\sin$ denotes the [[sine]], and $\pi$ denotes [[pi]].
    256 bytes (34 words) - 05:49, 6 June 2016
  • Anger three-term recurrence
    where $\textbf{J}_{\nu}$ denote the [[Anger function]], $\pi$ denotes [[pi]], and $\sin$ denotes [[sine]].
    310 bytes (46 words) - 05:50, 6 June 2016
  • Anger derivative recurrence
    where $\mathbf{J}_{\nu}$ denotes the [[Anger function]].
    218 bytes (31 words) - 05:50, 6 June 2016
  • Loggamma
    The loggamma function $\log \Gamma$ is defined by the [[principal branch]] of where $\log$ denotes the [[logarithm]] and $\Gamma$ denotes the [[gamma]] function.
    412 bytes (55 words) - 18:32, 24 May 2016
  • Contour integral representation of reciprocal gamma
    ...] function, $\pi$ denotes [[pi]], and $e^{-t}$ denotes the [[exponential]] function.
    480 bytes (63 words) - 07:17, 16 June 2016
  • Barnes G at z+1 in terms of Barnes G and gamma
    ...e $G$ denotes the [[Barnes G]] function and $\Gamma$ denotes the [[gamma]] function.
    226 bytes (30 words) - 12:52, 17 September 2016
  • Ramanujan tau is multiplicative
    [[Ramanujan tau]] is a [[multiplicative function]].
    134 bytes (13 words) - 00:53, 23 December 2016
  • Functional equation for Riemann xi
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann xi|next=Riemann-Land
    312 bytes (36 words) - 15:27, 18 March 2017
  • Generating function for partition function
    where $p(k)$ denotes the [[partition]] function. ...witz|author2=Irene A. Stegun|prev=Partition|next=Closed form for partition function with sinh}}: $24.2.1 \mathrm{I}.B.$
    541 bytes (72 words) - 20:34, 26 June 2016
  • Bolzano function is continuous
    The [[Bolzano function]] is [[continuous]].
    126 bytes (12 words) - 17:10, 23 June 2016
  • Cellérier function is continuous
    The [[Cellérier function]] is [[continuous]].
    129 bytes (13 words) - 17:12, 23 June 2016
  • Darboux function is continuous
    The [[Darboux function]] is [[continuous]] on $\mathbb{R}$.
    142 bytes (15 words) - 17:14, 23 June 2016
  • Knopp function is continuous
    The [[Knopp function]] $K_{a,b}$ is [[continuous]] on $\mathbb{R}$ for $a \in (0,1)$ and $ab>1$.
    179 bytes (23 words) - 03:31, 27 October 2016
  • McCarthy function is continuous
    The [[McCarthy function]] is [[continuous]] on $\mathbb{R}$.
    143 bytes (15 words) - 13:40, 17 November 2016
  • The Petr function is nowhere differentiable
    The [[Petr function]] is [[nowhere differentiable]] on $(0,1)$.
    146 bytes (14 words) - 20:34, 25 June 2017
  • Riemann function is continuous
    The [[Riemann function]] is [[continuous]].
    126 bytes (12 words) - 03:27, 6 July 2016
  • Schwarz function is continuous
    Let $M>0$. The [[Schwarz function]] is [[continuous]] on $(0,M)$.
    148 bytes (16 words) - 17:46, 20 September 2016
  • Van der Waerden function is continuous
    The [[van der Waerden function]] is [[continuous]].
    134 bytes (14 words) - 03:17, 6 July 2016
  • Derivative of inverse error function
    where $\mathrm{erf}^{-1}$ denotes the [[inverse error function]], $\pi$ denotes [[pi]], and $\exp$ denotes the [[exponential]].
    364 bytes (48 words) - 04:38, 16 September 2016
  • Relationship between logarithm and Mangoldt
    ...s that $d$ is a [[divisor]] of $n$, and $\Lambda$ denotes the [[Mangoldt]] function.
    315 bytes (42 words) - 16:31, 16 June 2016
  • Airy zeta function at 2
    ...m{Ai}}$ denotes the [[Airy zeta function]], $\Gamma$ denotes the [[gamma]] function, and $\pi$ denotes [[pi]].
    323 bytes (37 words) - 02:20, 2 November 2016
  • Fibonacci zeta at 1 is irrational
    ...ant]]) is an [[irrational number]], where $F$ denotes the [[Fibonacci zeta function]].
    234 bytes (28 words) - 17:37, 19 August 2016
  • Q-derivative of q-Cosine
    ...Cos|$q$-Cosine function]], and $\mathrm{Sin}$ denotes the [[Q-Sin|$q$-Sine function]].
    450 bytes (59 words) - 23:29, 26 June 2016
  • Q-Gamma at 1
    where $\Gamma_q$ denotes the [[Q-Gamma|$q$-gamma]] function.
    191 bytes (22 words) - 17:53, 17 October 2016
  • Relation between polygamma and Hurwitz zeta
    ...^{(m)}$ denotes the [[polygamma]] and $\zeta$ denotes the [[Hurwitz zeta]] function.
    253 bytes (33 words) - 06:34, 11 June 2016
  • Hurwitz zeta absolute convergence
    The [[Hurwitz zeta]] function $\zeta(s,a)$ is [[absolutely convergent]] for all $s$ with $\mathrm{Re}(s)>
    223 bytes (30 words) - 07:12, 16 June 2016
  • Trigamma
    The trigamma function $\psi^{(1)}$ is defined by where $\log \Gamma$ denotes the [[loggamma]] function.
    384 bytes (49 words) - 03:11, 21 December 2016
  • Euler-Jackson q-difference operator
    ...} \setminus \{1\}$. The Euler-Jackson $q$-difference operator applied to a function $f$ is given by the formula
    174 bytes (32 words) - 20:04, 3 June 2016
  • Book:Aleksandar Ivić/The Riemann Zeta-Function
    {{Book|The Riemann Zeta-Function: Theory and Applications|1985|Dover Publications, Inc|0-486-42813-3|Aleksan :: 12.4. The Generalised von Mangoldt Function and the Möbius Function
    5 KB (554 words) - 16:39, 21 June 2016
  • Book:Andrew Gray/A Treatise on Bessel Functions
    ...ter IX: Relations between Bessel Functions and Legendre Functions. Green's Function : Appendix I: Formulae for the Gamma Function and the Hypergeometric Function
    2 KB (220 words) - 19:38, 21 June 2017
  • Book:Andrew Gray/A Treatise on Bessel Functions/Second Edition
    * [[Definition:Bessel Function|Bessel Functions]] ...ter IX: Relations between Bessel Functions and Legendre Functions. Green's Function
    2 KB (212 words) - 16:39, 21 June 2016
  • Book:F.E. Relton/Applied Bessel Functions
    * [[Definition:Bessel Function|Bessel Functions]] : I. The Error Function; Beta and Gamma Functions
    908 bytes (110 words) - 16:40, 21 June 2016
  • Book:Ian N. Sneddon/Special Functions of Mathematical Physics and Chemistry
    ::5. The gamma function and related functions :::[[Error function|$(5.11)$]]
    3 KB (300 words) - 03:07, 25 June 2017
  • Book:Larry C. Andrews/Special Functions of Mathematics for Engineers
    * [[Definition:Special Function|Special Functions]] : Chapter 2. The Gamma Function and Related Functions
    7 KB (681 words) - 21:57, 3 June 2016
  • Chain rule for derivatives
    ...nd $g$ be differentiable functions for which we may define the [[composite function]] $f \circ g$. Then the following formula holds:
    493 bytes (71 words) - 17:22, 27 June 2016
  • Polar coordinates
    ...efinition of [[tangent]] and application of the [[arctan|inverse tangent]] function.
    620 bytes (88 words) - 17:23, 27 June 2016
  • Logarithm (multivalued)
    The (multivalued) logarithm function $\mathrm{Log} \colon \mathbb{C} \rightarrow \mathscr{P}\left( \mathbb{C} \r
    1 KB (139 words) - 19:33, 25 June 2017
  • Series for log(z+a) for positive a and Re(z) greater than -a
    ...greater than 1|next=Limit at infinity of logarithm times reciprocal power function is zero}}: $4.1.29$
    587 bytes (82 words) - 17:28, 27 June 2016
  • Book:Arthur Erdélyi/Higher Transcendental Functions Volume I
    :1.1. Definition of the gamma function ...t of a factorial, exponential, and a rising factorial|$(2)$]] (and [[Gamma function written as infinite product|$(2)$]]
    10 KB (1,331 words) - 06:07, 4 March 2018
  • Gamma(z) as integral of a power of log(1/t) for Re(z) greater than 0
    where $\Gamma$ denotes the [[gamma]] function and $\log$ denotes the [[logarithm]].
    559 bytes (71 words) - 20:56, 3 March 2018
  • Gamma function written as a limit of a factorial, exponential, and a rising factorial
    where $\Gamma$ denotes the [[gamma]] function. ...(z) as integral of a power of log(1/t) for Re(z) greater than 0|next=Gamma function written as infinite product}}: §1.1 (2)
    603 bytes (87 words) - 20:56, 3 March 2018
  • Gamma function written as infinite product
    where $\Gamma$ denotes the [[gamma]] function. ...Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Gamma function written as a limit of a factorial, exponential, and a rising factorial|next
    791 bytes (102 words) - 20:56, 3 March 2018
  • Reciprocal gamma written as an infinite product
    where $\dfrac{1}{\Gamma}$ is the [[reciprocal gamma]] function, and $\gamma$ is the [[Euler-Mascheroni constant]]. ...on|author2=George Neville Watson|prev=Euler-Mascheroni constant|next=Gamma function written as infinite product}}: $\S 12 \cdot 11$
    1 KB (138 words) - 20:56, 3 March 2018
  • Erf of conjugate is conjugate of erf
    where $\mathrm{erf}$ denotes the [[error function]] and $\overline{z}$ denotes the [[complex conjugate]]. ...atical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Error function is odd|next=findme}}: 7.1.10
    396 bytes (49 words) - 05:03, 5 June 2016
  • Book:Arthur Erdélyi/Higher Transcendental Functions Volume III
    ::::14.6.2. The modular function $\mathcal{J}(z)$ :::17.1. Elementary functions of number theory generated by Riemann's zeta function
    5 KB (544 words) - 05:44, 4 March 2018
  • Book:Gabor Szegő/Orthogonal Polynomials/Fourth Edition
    ::1.4. Orthogonality; weight function; vectors in function spaces ::1.7. The Gamma function
    3 KB (352 words) - 02:58, 15 July 2018
  • Book:G.H. Hardy/The General Theory Of Dirichlet's Series
    ...FOR THE SUM OF THE COEFFICIENTS OF A DIRICHLET'S SERIES: THE ORDER OF THE FUNCTION REPRESENTED BY THE SERIES
    819 bytes (110 words) - 23:27, 17 March 2017
  • Continued fraction for 1/sqrt(pi) integral from -infinity to infinity of e^(-t^2)/(z-t) dt
    ...zeros of the [[Hermite polynomials]], and $H_k^{(n)}$ denote the [[weight function]] for the Hermite polynomials.
    910 bytes (135 words) - 21:14, 6 June 2016
  • Limit of erf when z approaches infinity and the modulus of arg(z) is less than pi/4
    where $\mathrm{erf}$ denotes the [[error function]].
    531 bytes (70 words) - 02:18, 6 June 2016
  • Anger of integer order is Bessel J
    ...{J}_n$ denotes an [[Anger function]] and $J_n$ denotes a [[Bessel J|Bessel function of the first kind]]. ...4|Milton Abramowitz|author2=Irene A. Stegun|prev=Anger function|next=Weber function}}: 12.3.2
    389 bytes (57 words) - 04:07, 6 June 2016
  • Versine
    The versine function $\mathrm{versin} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by th where $ \cos$ denotes the [[cosine]] function.
    734 bytes (92 words) - 02:33, 5 January 2017
  • Coversine
    The coversine function $\mathrm{coversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by where $\sin$ denotes the [[sine]] function.
    680 bytes (84 words) - 04:27, 3 October 2016
  • Haversine
    The haversine function $\mathrm{haversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
    401 bytes (46 words) - 03:45, 28 March 2017
  • Exsecant
    The exsecant function $\mathrm{exsec}$ is defined by
    550 bytes (68 words) - 04:11, 28 March 2017
  • Relationship between Anger function and Bessel J sub nu
    #REDIRECT [[Relationship between Anger function and Bessel J]]
    62 bytes (8 words) - 05:51, 6 June 2016
  • Euler's formula
    where $e^{iz}$ denotes the [[exponential function]], $\cos$ denotes the [[cosine]], $i$ denotes the [[imaginary number]], and
    631 bytes (99 words) - 00:20, 23 December 2016
  • E^x is less than 1/(1-x) for nonzero real x less than 1
    where $e^x$ denotes the [[exponential function]].
    465 bytes (69 words) - 00:32, 23 December 2016
  • Gauss' formula for gamma function
    where $\Gamma$ denotes the [[gamma]] function and $n!$ denotes the [[factorial]].
    462 bytes (62 words) - 07:03, 8 June 2016
  • Book:Edward Charles Titchmarch/The Zeta-Function of Riemann
    #REDIRECT [[Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann]]
    73 bytes (9 words) - 19:39, 9 June 2016
  • Number theory functions footer
    <div class="grid"><center>[[File:Chebthetathumb.png|45px|link=Chebyshev theta function]]<br /> [[Chebyshev theta function|Chebyshev $\vartheta$]]</center></div>
    2 KB (233 words) - 11:15, 11 January 2017
  • Paper:Harry Bateman/Some Properties of a certain Set of Polynomials
    :1. The generating function. :2. Transformation of the generating function.
    654 bytes (90 words) - 01:59, 22 June 2016
  • Hankel H (1) in terms of csc and Bessel J
    ...otes the [[imaginary number]], and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
    646 bytes (95 words) - 04:09, 11 June 2016
  • Hankel H (2) in terms of csc and Bessel J
    ...$\csc$ denotes the [[cosecant]], $J_{-\nu}$ denotes the [[Bessel J|Bessel function of the first kind]], and $e^{\nu \pi i}$ denotes the [[exponential]].
    664 bytes (100 words) - 04:50, 11 June 2016
  • Relationship between Bessel J sub n and Bessel J sub -n
    where $J_{-n}$ denotes the [[Bessel J|Bessel function of the first kind]].
    455 bytes (70 words) - 04:52, 11 June 2016
  • Relationship between Bessel Y sub n and Bessel Y sub -n
    where $Y_{-n}$ denotes the [[Bessel Y|Bessel function of the second kind]].
    421 bytes (62 words) - 04:54, 11 June 2016
  • Value of polygamma at 1
    ..., $m!$ denotes the [[factorial]], and $\zeta$ denotes the [[Riemann zeta]] function.
    482 bytes (62 words) - 22:45, 17 March 2017
  • Polygamma multiplication formula
    where $\psi^{(m)}$ denotes the [[polygamma]] function and $\log$ denotes the [[logarithm]].
    580 bytes (77 words) - 22:51, 17 March 2017
  • Book:Edmund Taylor Whittaker/A course of modern analysis/Third edition
    ::Chapter XII The Gamma Function ::Chapter XIII The Zeta Function of Riemann
    2 KB (229 words) - 16:39, 21 June 2016
  • Gamma recurrence relation
    where $\Gamma$ denotes the [[gamma function]].
    355 bytes (46 words) - 02:28, 12 June 2016
  • The Euler-Mascheroni constant exists
    ...e\sum_{k=1}^{\infty} \dfrac{1}{k^2}$ converges (it is the [[Riemann zeta]] function evaluated at $z=2$), we can conclude that $\displaystyle\sum_{k=1}^{\infty}
    2 KB (279 words) - 20:31, 20 June 2016
  • Paper:Carl-Erik Fröberg/On the prime zeta function
    {{Book|On the prime zeta function|1968|BIT Numerical Mathematics||Carl-Erik Fröberg}}
    209 bytes (26 words) - 19:27, 15 June 2016
  • Paper:Matilde Lalín/Secant zeta functions
    ::[[Absolute convergence of secant zeta function|Theorem 1]]<br />
    365 bytes (44 words) - 20:25, 20 June 2016
  • Absolute convergence of secant zeta function
    The series defining the [[secant zeta function]] $\psi_s(z)$ converges absolutely in the following cases:
    430 bytes (56 words) - 06:09, 16 June 2016
  • Derivative of Bessel J with respect to its order
    ...t kind]], $\log$ denotes the [[logarithm]], $\psi$ denotes the [[digamma]] function, and $k!$ denotes the [[factorial]].
    685 bytes (98 words) - 22:45, 19 June 2016
  • Derivative of Bessel Y with respect to its order
    ...$\cot$ denotes the [[cotangent]], $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]], $\pi$ denotes [[pi]], and $\csc$ denotes the [[cosecan
    774 bytes (118 words) - 00:50, 28 August 2016
  • Identity written as a sum of Möbius functions
    where $\mu$ denotes the [[Möbius function]]. ...nn zeta as a sum of Möbius function for Re(z) greater than 1|next=Möbius function is multiplicative}}: $24.3.1 \mathrm{I}.B.$
    487 bytes (69 words) - 01:33, 22 June 2016
  • Möbius function is multiplicative
    The [[Möbius function]] is a [[multiplicative function]].
    332 bytes (41 words) - 01:32, 22 June 2016
  • Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2
    ...tes the [[Euler totient|totient]] and $\zeta$ denotes the [[Riemann zeta]] function.
    518 bytes (68 words) - 04:49, 22 June 2016
  • Euler totient is multiplicative
    The [[Euler totient|totient]] is a [[multiplicative]] function.
    323 bytes (36 words) - 04:50, 22 June 2016
  • Beta as improper integral
    where $B$ denotes the [[beta]] function.
    517 bytes (72 words) - 20:57, 3 March 2018
  • Beta is symmetric
    where $B$ denotes the [[beta]] function.
    765 bytes (117 words) - 20:57, 3 March 2018
  • Beta as product of gamma functions
    where $B$ denotes the [[beta]] function and $\Gamma$ denotes the [[gamma]] function.
    475 bytes (67 words) - 20:58, 3 March 2018
  • Digamma at 1
    where $\psi$ denotes the [[digamma]] function and $\gamma$ denotes the [[Euler-Mascheroni constant]].
    578 bytes (67 words) - 23:22, 3 March 2018
  • Digamma at z+n
    where $\psi$ denotes the [[digamma]] function.
    472 bytes (59 words) - 23:22, 3 March 2018
  • Cellérier function is nowhere differentiable
    The [[Cellérier function]] is [[nowhere differentiable]].
    141 bytes (14 words) - 17:12, 23 June 2016
  • Darboux function is nowhere differentiable
    The [[Darboux function]] is [[nowhere differentiable]] on $\mathbb{R}$.
    154 bytes (16 words) - 17:14, 23 June 2016
  • Faber F1 is continuous
    The [[Faber F1]] function is [[continuous]].
    127 bytes (13 words) - 17:16, 23 June 2016
  • Euler product for Riemann zeta
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann zeta|next=Series for
    727 bytes (88 words) - 05:00, 16 September 2016
  • Faber F1 is nowhere differentiable
    The [[Faber F1]] function is [[nowhere differentiable]].
    139 bytes (14 words) - 17:18, 23 June 2016
  • Faber F2 is nowhere differentiable
    The [[Faber F2]] function is [[nowhere differentiable]].
    139 bytes (14 words) - 17:17, 23 June 2016
  • Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1
    ...e $\zeta$ denotes the [[Riemann zeta function]] and $\mu$ is the [[Möbius function]]. ...ical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Möbius function|next=Identity written as a sum of Möbius functions}}: $24.3.1. \mathrm{I}.
    506 bytes (69 words) - 01:34, 22 June 2016
  • Book:Victor Kac/Quantum Calculus
    :12 Classical Partition Function and Euler's Product Formula
    2 KB (195 words) - 05:16, 21 January 2017
  • Error functions footer
    <div class="grid"><center>[[Error function|<randomimagebycategory categories="Errorglyph" width="45" />]]<br /> [[Error function]]</center></div>
    624 bytes (80 words) - 21:57, 6 July 2016
  • Erfi
    The imaginary error function $\mathrm{erfi}$ is defined by where $\mathrm{erf}$ denotes the [[error function]].
    413 bytes (54 words) - 23:10, 23 October 2016
  • Jinc
    The $\mathrm{jinc}$ function is defined by where $J_1$ denotes the [[Bessel J|Bessel function of the first kind]].
    479 bytes (66 words) - 04:03, 22 September 2016
  • Inverse Gudermannian
    ...ian $\mathrm{gd}^{-1}$ is the [[inverse function]] of the [[Gudermannian]] function. It may be defined by the following formula for $x \in \mathbb{R}$:
    966 bytes (122 words) - 23:10, 11 June 2016
  • Q-exponential e sub 1/q
    The $q$-exponential $e_{\frac{1}{q}}$ is an [[entire]] function and is defined for $0 < |q| < 1$ by
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  • Q-exponential E sub 1/q
    The $E_{\frac{1}{q}}$ function is defined by the formula
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  • Derivative of arcsin
    where $\arcsin$ denotes the [[arcsin|inverse sine]] function.
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  • Derivative of arcsec
    where $\mathrm{arcsec}$ is the [[arcsec|inverse secant]] function.
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  • Derivative of arccot
    where $\mathrm{arccot}$ denotes the [[arccot|inverse cotangent]] function.
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  • Pythagorean identity for sin and cos
    where $\sin$ denotes the [[sine]] function and $\cos$ denotes the [[cosine]] function.
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  • Gompertz constant
    where $e$ denotes the base of the [[exponential function]] and $\mathrm{Ei}$ denotes the [[exponential integral Ei]].
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  • Series for erf with exponential factored out
    where $\mathrm{erf}$ denotes the [[error function]] and $\pi$ denotes [[pi]].
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  • Taylor series for error function
    where $\mathrm{erf}$ denotes the [[error function]] and $\pi$ denotes [[pi]], and $k!$ denotes the [[factorial]]. From the [[Taylor series of the exponential function]],
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  • Scorer Gi
    The Scorer $\mathrm{Gi}$ function is a solution of the [[differential equation]] $y''(x)-x y(x)=\dfrac{1}{\pi
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  • Relationship between Scorer Gi and Airy functions
    ...enotes the [[Airy Ai]] function, and $\mathrm{Bi}$ denotes the [[Airy Bi]] function.
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  • Scorer Hi
    The Scorer $\mathrm{Hi}$ function is a solution of the [[differential equation]] $y''(x)-x y(x)=\dfrac{1}{\pi
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  • Relationship between Scorer Hi and Airy functions
    ...enotes the [[Airy Ai]] function, and $\mathrm{Bi}$ denotes the [[Airy Bi]] function.
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  • Bolzano function
    A Bolzano function $B \colon [a,b] \rightarrow [c,d]$ is is defined as the limit of a sequence The Bolzano function is defined by the pointwise limit
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  • Bolzano function is nowhere differentiable
    The [[Bolzano function]] is [[nowhere differentiable]].
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  • Cellérier function
    Let $a>1000$. The Cellérier function is defined as [[Cellérier function is continuous]]<br />
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  • Riemann function
    The Riemann function is the function $R \colon \mathbb{R} \rightarrow \mathbb{R}$ defined by [[Riemann function is continuous]]<br />
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  • Darboux function
    The Darboux function is defined by where $\sin$ denotes the [[sine]] function.
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  • Schwarz function
    ...r \cdot \rfloor$ denotes the [[floor]] function and let $M>0$. The Schwarz function $S \colon (0,M) \rightarrow \mathbb{R}$ is defined by [[Schwarz function is continuous]]<br />
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  • Blancmange function
    #REDIRECT [[Takagi function]]
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  • Takagi function is continuous
    The [[Takagi function]] is [[continuous]].
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  • Van der Waerden function
    The van der Waerden function $V \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined by the formula where $\mathrm{dist}_{\mathbb{Z}}$ denotes the [[distance to integers]] function.
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  • Faber F1
    The Faber function $F_1$ is defined by
    526 bytes (72 words) - 03:32, 6 July 2016
  • Faber F2
    The Faber function $F_2$ is defined by
    523 bytes (71 words) - 03:32, 6 July 2016
  • Faber functions
    #REDIRECT [[Faber function F1]]
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  • Knopp function
    Let $a \in (0,1)$ $ab > 1$. Define the Knopp function $K \colon \mathbb{R} \rightarrow \mathbb{R}$ by where $\mathrm{dist}_{\mathbb{Z}}$ denotes the [[distance to integers]] function.
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  • Knopp function is nowhere differentiable
    The [[Knopp function]] $K_{a,b}$ is [[nowhere differentiable]] on $\mathbb{R}$ for $a \in (0,1)$
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  • Petr function
    ...1}^{\infty} \dfrac{a_k}{10^k}$, where $a_k \in \{0,1,\ldots,9\}$. The Petr function $P_K \colon [0,1] \rightarrow \mathbb{R}$ is defined by [[The Petr function is continuous]]<br />
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  • McCarthy function
    The McCarthy function $M$ is defined by [[McCarthy function is continuous]]<br />
    493 bytes (72 words) - 13:39, 17 November 2016
  • Multiple gamma function
    where $\zeta_N$ denotes the [[Barnes zeta function]].
    211 bytes (35 words) - 18:32, 24 May 2016
  • Elliptic gamma function
    The elliptic gamma function is defined by
    204 bytes (32 words) - 18:54, 24 May 2016
  • Gamma(1)=1
    where $\Gamma$ denotes the [[gamma]] function.
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  • Ramanujan theta function
    The Ramanujan theta function, $f$, is defined for $|ab|<1$ by
    379 bytes (61 words) - 16:02, 10 July 2017
  • Distance to integers
    Define the function $\mathrm{dist}_{\mathbb{Z}} \colon \mathbb{R} \rightarrow \mathbb{R}$ by where $\inf$ denotes the [[infimum]]. This function can be computed using the [[floor]] and [[ceiling]] functions:
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  • Faber F2 is continuous
    The [[Faber F2]] function is [[continuous]].
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  • Stieltjes constants
    [[Laurent series of the Riemann zeta function]]<br />
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  • Book:Harris Hancock/Lectures on the theory of elliptic functions
    :::1. One-valued function. Regular function. Zeros :::7. A one-valued function that is regular at all points of the plane is a constant
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  • Jacobi theta 2
    Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_2$ function is defined by where $\cos$ denotes the [[cosine]] function.
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  • Jacobi theta 3
    Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_3$ function is defined by where $\cos$ denotes the [[cosine]] function.
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  • Jacobi theta 4
    Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_4$ function is defined by where $\cos$ denotes the [[cosine]] function.
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  • Sum of sum of divisors function equals product of Riemann zeta for Re(z) greater than k+1
    where $\sigma_n$ denotes the [[sum of divisors]] function and $\zeta$ denotes the [[Riemann zeta]].
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  • Closed form for partition function
    #REDIRECT [[Closed form for partition function with sinh]]
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  • Recurrence relation for partition function
    #REDIRECT [[Pure recurrence relation for partition function]]
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  • Recurrence relation for partition function with sum of divisors
    ...the [[partition]] function and $\sigma_1$ denotes the [[sum of divisors]] function. ...tion function|next=Sum of divisors functions written in terms of partition function}}: $24.2.1 \mathrm{II}.A.$
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  • Sum of divisors functions written in terms of partition function
    ...$ denotes the [[sum of divisors]] function and $p$ denotes the [[partition function]]. ...tition function with sum of divisors|next=Asymptotic formula for partition function}}: $24.2.1 \mathrm{II}.B.$
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  • Asymptotic formula for partition function
    where $p$ denotes the [[partition]] function, $\exp$ denotes the [[exponential]], and $\pi$ denotes [[pi]]. ...ene A. Stegun|prev=Sum of divisors functions written in terms of partition function|next=findme}}: $24.2.1 \mathrm{III}$
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  • Hypergeometric 1F0
    The hypergeometric ${}_1F_0$ function is defined by the series
    316 bytes (41 words) - 06:04, 10 January 2017
  • Hypergeometric 2F1
    The (Gauss) hypergeometric ${}_2F_1$ function (often written simply as $F$) is defined by the series ...neq 0, -1, -2, \ldots$. It is a special case of the [[hypergeometric pFq]] function.
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  • Limit of (1/Gamma(c))*2F1(a,b;c;z) as c approaches -m
    where $\Gamma$ denotes the [[gamma]] function, $(a)_{m+1}$ denotes the [[Pochhammer]] symbol, and ${}_2F_1$ denotes the [
    590 bytes (79 words) - 23:15, 12 July 2016
  • Riemann zeta as contour integral
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann zeta as integral of
    764 bytes (111 words) - 23:42, 17 March 2017
  • Integral of monomial times Bessel J
    ...l J|Bessel function of the first kind]] and $\Gamma$ denotes the [[gamma]] function.
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  • Integral of Bessel J for Re(nu) greater than -1
    where $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
    505 bytes (72 words) - 16:56, 27 June 2016
  • Integral of Bessel J for nu=2n
    where $J_{2n}$ denotes the [[Bessel J|Bessel function of the first kind]].
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  • Integral of Bessel J for nu=2n+1
    where $J_{2n+1}$ denotes the [[Bessel J|Bessel function of the first kind]].
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  • Integral of Bessel J for nu=n+1
    where $J_{n+1}$ denotes the [[Bessel J|Bessel function of the first kind]].
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  • Integral of Bessel J for nu=1
    where $J_1$ denotes the [[Bessel J|Bessel function of the first kind]].
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  • Riccati-Bessel S
    The Riccati-Bessel function $S_n$ is defined by the formula ...$\pi$ denotes [[pi]] and $J_{n+\frac{1}{2}}$ denotes the [[Bessel J|Bessel function of the first kind]].
    287 bytes (43 words) - 21:02, 27 June 2016
  • Hypergeometric 1F1
    ...$ (sometimes denoted by $M$, sometimes called the confluent hypergeometric function of the first kind) is defined by the series
    568 bytes (93 words) - 20:31, 17 June 2017
  • Hypergeometric 1F2
    [[Relationship between Struve function and hypergeometric pFq]]<br />
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  • Series for log(Riemann zeta) in terms of Mangoldt function
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Series for log(riemann zeta)
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  • Logarithmic derivative of Riemann zeta in terms of series over primes
    ...function|next=Logarithmic derivative of Riemann zeta in terms of Mangoldt function}}: § Introduction $(2{'}{'})$
    578 bytes (77 words) - 02:17, 1 July 2017
  • Logarithmic derivative of Riemann zeta in terms of Mangoldt function
    ...\zeta$ denotes the [[Riemann zeta]] and $\Lambda$ denotes the [[Mangoldt]] function. * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Logarithmic derivative of Ri
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  • Van der Waerden function is nowhere differentiable
    The [[van der Waerden function]] is [[nowhere differentiable]].
    146 bytes (15 words) - 03:18, 6 July 2016
  • Riemann function is almost nowhere differentiable
    The [[Riemann function]] is [[nowhere differentiable]] except at points of the form $\pi \dfrac{2p
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  • Continuous nowhere differentiable functions footer
    <div class="grid2"><center>[[Darboux function|<randomimagebycategory categories="darbouxglyph" width=45 />]] <br /> [[Darboux function]]</center></div>
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  • Closed formula for physicist's Hermite polynomials
    ...ynomials]], $\left\lfloor \frac{n}{2} \right\rfloor$ denotes the [[floor]] function, and $k!$ denotes the [[factorial]]. * {{BookReference|Special Functions|1960|Earl David Rainville|prev=Generating function for Hermite (physicist) polynomials|next=findme}}: $103. (2)$
    568 bytes (73 words) - 23:33, 8 July 2016
  • Series for q-sin sub q
    where $\sin_q$ denotes the [[q-sin sub q|$\sin_q$]] function.
    408 bytes (56 words) - 15:39, 11 July 2016
  • Omega constant
    This means it equals $W(1)$, where $W$ denotes the [[Lambert W]] function.
    226 bytes (33 words) - 00:41, 5 August 2016
  • Digamma at 1/2
    where $\psi$ denotes the [[digamma]] function, $\gamma$ denotes the [[Euler-Mascheroni constant]], and $\log$ denotes the
    461 bytes (54 words) - 00:50, 9 August 2016
  • Digamma at n+1/2
    where $\psi$ denotes the [[digamma]] function and $\gamma$ denotes the [[Euler-Mascheroni constant]].
    523 bytes (59 words) - 00:52, 9 August 2016
  • Binet's formula
    ...ence|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Fibonacci zeta function|next=Fibonacci zeta in terms of a sum of binomial coefficients}}
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  • Fibonacci zeta in terms of a sum of binomial coefficients
    where $F(z)$ denotes the [[Fibonacci zeta function]], $\displaystyle{{-z} \choose j}$ denotes a [[binomial coefficient]], and * {{PaperReference|The Fibonacci Zeta Function|1976|Maruti Ram Murty|prev=Binet's formula|next=findme}}
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  • Paper:Maruti Ram Murty/The Fibonacci Zeta Function
    {{Book|The Fibonacci Zeta Function|1976|Journal of the London Mathematical Society||Maruti Ram Murty}} [[Fibonacci zeta function]] <br />
    387 bytes (52 words) - 00:28, 24 May 2017
  • Normalized sinc
    The normalized sinc function $\mathrm{sinc}_{\pi}$ is defined by
    267 bytes (37 words) - 02:22, 16 September 2016
  • Reciprocal Riemann zeta
    ...fined by $\dfrac{1}{\zeta(z)},$ where $\zeta$ denotes the [[Riemann zeta]] function.
    266 bytes (34 words) - 03:54, 16 September 2016
  • Reciprocal Riemann zeta in terms of Mobius
    where $\zeta$ denotes the [[Riemann zeta]] and $\mu$ denotes the [[Möbius]] function.
    449 bytes (57 words) - 19:31, 21 June 2017
  • Schwarz function is nowhere differentiable on a dense subset
    Let $M>0$. The [[Schwarz function]] is [[nowhere differentiable]] on a [[dense]] subset of $(0,M)$.
    182 bytes (21 words) - 17:47, 20 September 2016
  • Derivative of prime zeta
    where $P$ denotes the [[prime zeta P|prime zeta]] function and $\log$ denotes the [[logarithm]]. Recall the definition of the prime zeta function:
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  • K-function
    The $K$-function is defined by ...ient]], $\log$ denotes the [[logarithm]], and $\Gamma$ denotes the [[gamma function]].
    461 bytes (59 words) - 19:40, 25 September 2016
  • Hyperfactorial in terms of K-function
    where $H$ denotes the [[hyperfactorial]] and $K$ denotes the [[K-function]].
    205 bytes (25 words) - 19:40, 25 September 2016
  • Fresnel S in terms of erf
    ...$ denotes the [[imaginary number]], and $\mathrm{erf}$ denotes the [[error function]].
    425 bytes (58 words) - 17:17, 5 October 2016
  • Fresnel S is odd
    The [[Fresnel S]] function is an [[odd function]].
    133 bytes (15 words) - 17:13, 5 October 2016
  • Fresnel C is odd
    [[Fresnel C]] is an [[odd function]].
    120 bytes (13 words) - 17:23, 5 October 2016
  • Fresnel C in terms of erf
    ...$ denotes the [[imaginary number]], and $\mathrm{erf}$ denotes the [[error function]].
    425 bytes (57 words) - 17:26, 5 October 2016
  • Beta in terms of power of t over power of (1+t)
    where $B$ denotes the [[beta]] function.
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  • Derivative of erfi
    ...unction]], $\pi$ denotes [[pi]], and $e^{z^2}$ denotes the [[exponential]] function.
    340 bytes (44 words) - 23:12, 23 October 2016
  • Paper:Richard E. Crandall/On the quantum zeta function
    {{Book|On the quantum zeta function|1996|Journal of Physics A: Mathematical and General||Richard E. Crandall}}
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  • Thomae function is continuous at irrationals
    The [[Thomae function]] is [[continuous]] at all [[irrational number|irrational numbers]].
    173 bytes (18 words) - 00:34, 9 December 2016
  • McCarthy function is nowhere differentiable
    The [[McCarthy function]] is [[nowhere differentiable]] on $\mathbb{R}$.
    155 bytes (16 words) - 13:40, 17 November 2016
  • Riemann zeta as integral of monomial divided by an exponential
    where $\zeta$ denotes the [[Riemann zeta]] function and $e^t$ denotes the [[exponential]]. ...itchmarsh|prev=Logarithmic derivative of Riemann zeta in terms of Mangoldt function|next=Riemann zeta as contour integral}}: § Introduction $(3)$
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  • Arcsin as inverse sine
    ...ac{\pi}{2} \right]$ is the [[inverse function]] of the restricted [[sine]] function $\sin \colon \left[ -\dfrac{\pi}{2}, \dfrac{\pi}{2} \right] \rightarrow [-1
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  • Arccos as inverse cosine
    ...ghtarrow [0,\pi]$ is the [[inverse function]] of the restricted [[cosine]] function $\cos \colon \left[0,\pi\right] \rightarrow [-1,1]$.
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  • Product of Weierstrass elementary factors is entire
    ...s elementary factors|Weierstrass elementary factor]] defines an [[entire]] function which has a zero at each $a_k$ and no other zeros. If a complex number $w$
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  • Thomae function is discontinuous at rationals
    The [[Thomae function]] is discontinuous at all [[rational number|rational numbers]].
    168 bytes (18 words) - 00:34, 9 December 2016
  • Q-shifted factorial
    * {{PaperReference|The q-gamma function for q greater than 1|1980|Daniel S. Moak|prev=Q-Gamma|next=Q-Gamma at z+1}}
    997 bytes (133 words) - 01:14, 25 December 2018
  • Book:George E. Andrews/Special Functions
    ::1.11 A Probabilistic Evaluation of the Beta Function ::1.12 The $p$-adic Gamma Function
    6 KB (697 words) - 20:59, 18 December 2016
  • Asymptotic behavior of Sievert integral
    ...^{-x}$ denotes the [[exponential]], and $\mathrm{erf}$ denotes the [[error function]].
    568 bytes (72 words) - 02:08, 21 December 2016
  • Bessel J in terms of Bessel-Clifford
    ...$ denotes [[Bessel J]] and $\mathcal{C}_n$ denotes the [[Bessel-Clifford]] function.
    295 bytes (41 words) - 10:44, 11 January 2017
  • Böhmer S
    The Böhmer $S$ function is defined by
    326 bytes (47 words) - 06:51, 10 January 2017
  • Clausen sine
    Let $s \in \mathbb{C}$. The Clausen sine function $\mathrm{Cl}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined as the
    471 bytes (66 words) - 19:44, 7 September 2020
  • Clausen cosine
    Let $s \in \mathbb{C}$. The Clausen cosine function $\tilde{\mathrm{Cl}}_s \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined
    521 bytes (72 words) - 18:56, 7 September 2020
  • Paper:Thomas Clausen/Uber die function sin(φ)+sin(2φ)/2^2+sin(3φ)/3^2+etc.
    {{Book|Uber die function sin(φ)+sin(2φ)/2^2+sin(3φ)/3^2+etc.|1832|Journal für die reine und ange
    286 bytes (39 words) - 06:38, 10 January 2017
  • Dirichlet function
    The Dirichlet function $D \colon \mathbb{R} \rightarrow \{0,1\}$ is defined by [[Dirichlet function is nowhere continuous]]<br />
    525 bytes (71 words) - 07:29, 10 January 2017
  • Dirichlet function is nowhere continuous
    The [[Dirichlet function]] is nowhere [[continuous]].
    136 bytes (13 words) - 07:31, 10 January 2017
  • Relationship between Bessel-Clifford and hypergeometric 0F1
    where $\mathcal{C}_n$ denotes the [[Bessel-Clifford]] function and ${}_0F_1$ denotes [[hypergeometric 0F1]].
    272 bytes (33 words) - 10:46, 11 January 2017
  • Derivative of Bessel-Clifford
    where $\mathcal{C}_n$ denotes the [[Bessel-Clifford]] function.
    242 bytes (32 words) - 10:48, 11 January 2017
  • Reciprocal gamma is entire
    The [[reciprocal gamma]] function is [[entire]].
    131 bytes (13 words) - 10:50, 11 January 2017
  • Riemann zeta at even integers
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann zeta as contour inte
    574 bytes (77 words) - 23:57, 17 March 2017
  • Functional equation for Riemann zeta
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann zeta at even integer
    536 bytes (70 words) - 00:00, 18 March 2017
  • Functional equation for Riemann zeta with cosine
    * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Functional equation for Riem
    508 bytes (66 words) - 15:18, 18 March 2017
  • Riemann-Landau xi is even
    [[Riemann-Landau xi]] is an [[even function]]. * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Riemann-Landau xi|next=findm
    268 bytes (28 words) - 15:29, 18 March 2017
  • Havercosine
    The havercosine function $\mathrm{havercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
    239 bytes (28 words) - 03:51, 28 March 2017
  • Covercosine
    The coversine function $\mathrm{coversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ defined by
    221 bytes (27 words) - 03:47, 28 March 2017
  • Vercosine
    The vercosine function $\mathrm{vercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by
    221 bytes (27 words) - 03:51, 28 March 2017
  • Hacovercosine
    The hacovercosine function $\mathrm{hacovercos} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined b
    241 bytes (28 words) - 03:50, 28 March 2017
  • Hacoversine
    The hacoversine function $\mathrm{hacoversin} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined b
    242 bytes (29 words) - 03:52, 28 March 2017
  • Paper:Daniel S. Moak/The q-gamma function for q greater than 1
    {{Book|The q-gamma function for q greater than 1|1980|Aequationes Mathematicae||Daniel S. Moak|}}
    351 bytes (44 words) - 00:18, 30 May 2017
  • Book:Yudell L. Luke/The Special Functions And Their Approximations, Volume I
    :II. The Gamma function and Related Functions ::2.4. The Logarithmic Derivative of the Gamma Function
    2 KB (244 words) - 02:02, 30 May 2017

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