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• Riemann-Siegel theta function
  The Riemann-Siegel theta function is defined by where $\Gamma$ denotes the [[Gamma function]] and $\log$ denotes the [[logarithm]].
  229 bytes (33 words) - 00:27, 21 March 2015
• Reciprocal zeta function
  ...eta function is $\dfrac{1}{\zeta(s)}$, where $\zeta$ is the [[Riemann zeta function]]. ...eta$ denotes the [[Riemann zeta function]], and $\mu$ denotes the [[Mobius function]].
  587 bytes (73 words) - 18:53, 24 May 2016
• Lefschetz zeta function
  Let $f$ be a function. The Lefschetz zeta function is
  244 bytes (44 words) - 18:52, 24 May 2016
• P-adic zeta function
  The $p$-adic zeta function is
  95 bytes (14 words) - 18:53, 24 May 2016
• Relationship between the exponential integral and upper incomplete gamma function
  ...integral E]] and $\Gamma$ denotes the [[incomplete gamma|incomplete gamma function]].
  268 bytes (36 words) - 00:16, 8 August 2016
• Partial derivative of beta function
  ...$\Gamma$ denotes the [[gamma function]], and $\psi$ denotes the [[digamma function]].
  397 bytes (62 words) - 15:32, 23 June 2016
• Arithmetic zeta function
  Let $X$ be a [[scheme]]. The arithmetic zeta function over $X$ is defined by
  166 bytes (26 words) - 18:51, 24 May 2016
• Artin-Mazur zeta function
  ...e the [[cardinality]] of the set $\mathrm{Fix}(f^n)$. The Artin-Mazur zeta function is
  441 bytes (74 words) - 18:52, 24 May 2016
• P-adic L function
  73 bytes (10 words) - 04:11, 12 April 2015
• Arakawa-Kaneko zeta function
  where $\Gamma$ denotes the [[gamma function]] and $\mathrm{Li}_k$ denotes the [[polylogarithm]]. ...$ and $\xi_k$ has [[analytic continuation]] to $\mathbb{C}$ as an [[entire function]].
  1 KB (140 words) - 17:22, 24 June 2016
• Barnes zeta function
  The Barnes zeta function is
  184 bytes (32 words) - 18:52, 24 May 2016
• Takagi function
  The Takagi function (also called the blancmange function) is defined by where $\mathrm{dist}_{\mathbb{Z}}$ denotes the [[distance to integers]] function.
  740 bytes (97 words) - 03:33, 6 July 2016
• Relationship between the exponential integral and incomplete gamma function
  ...[[Relationship between the exponential integral and upper incomplete gamma function]]
  95 bytes (11 words) - 03:42, 23 April 2015
• Meijer G-function
  ....youtube.com/watch?v=rZngIxZsxeA Mellin Barnes Integral for an Exponential Function]<br />
  111 bytes (16 words) - 02:03, 30 April 2015
• Relationship between Hurwitz zeta and gamma function
  ...a$ denotes the [[gamma function]] and $\zeta$ denotes the [[Hurwitz zeta]] function.
  310 bytes (42 words) - 07:13, 16 June 2016
• Laurent series of the Riemann zeta function
  where $\zeta$ denotes the [[Riemann zeta]] function and $\lambda_k$ denotes the [[Stieltjes constants]].
  328 bytes (42 words) - 05:02, 16 September 2016
• Complex conjugate of argument of error function
  where $\mathrm{erf}$ denotes the [[error function]] and $\overline{z}$ denotes the [[complex conjugate]].
  278 bytes (33 words) - 00:22, 8 August 2016
• Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta
  ..., $\log$ denotes the [[logarithm]], and $\zeta$ denotes the [[Riemann zeta function]].
  359 bytes (48 words) - 19:31, 15 June 2016
• Takagi function is nowhere differentiable
  The [[Takagi function]] is [[nowhere differentiable]].
  137 bytes (13 words) - 03:16, 6 July 2016
• Doubly periodic function
  ...\rightarrow \mathbb{C}$ is called doubly periodic if it has two [[periodic function|periods]] $\omega_1$ and $\omega_2$ such that $\dfrac{\omega_1}{\omega_2}$
  207 bytes (32 words) - 21:04, 6 June 2015
• Cantor function
  31 bytes (3 words) - 20:18, 21 May 2015
• Periodic function
  ...omega \in X$. This concept is related to the notion of a [[doubly periodic function]].
  215 bytes (39 words) - 21:03, 6 June 2015
• Weierstrass nowhere differentiable function
  The Weierstrass function is [[Weierstrass function is continuous]]<br />
  473 bytes (63 words) - 17:54, 25 June 2017
• Weierstrass function
  #REDIRECT [[Weierstrass nowhere differentiable function]]
  57 bytes (5 words) - 02:30, 22 May 2015
• Chebyshev theta function
  The Chebyshev $\vartheta$ function is
  531 bytes (72 words) - 02:18, 28 November 2016
• Chebyshev psi function
  The Chebyshev $\psi$ function is where $\Lambda$ denotes the [[Mangoldt function]].
  418 bytes (54 words) - 03:47, 22 June 2016
• Elliptic function
  A function $f$ is called elliptic if it is a [[doubly periodic function]] and it is [[meromorphic]]. <strong>Theorem:</strong> A nonconstant [[elliptic function]] has a [[fundamental pair of periods]].
  2 KB (259 words) - 00:00, 23 December 2016
• Anger function
  Let $\nu \in \mathbb{C}$. The Anger function $\mathbf{J}_{\nu}$ is defined by [[Relationship between Anger function and Bessel J sub nu]]<br />
  1 KB (193 words) - 04:05, 6 June 2016
• Relationship between Anger function and Bessel J
  ...{J}_n$ denotes an [[Anger function]] and $J_n$ denotes a [[Bessel J|Bessel function of the first kind]].
  278 bytes (42 words) - 20:27, 27 June 2016
• Weber function
  The Weber function is defined by [[Relationship between Weber function and Anger function]]<br />
  781 bytes (98 words) - 04:13, 6 June 2016
• Relationship between Weber function and Anger function
  ...u}$ denotes a [[Weber function]] and $\mathbf{J}_{\nu}$ denotes an [[Anger function]]. ...unction and Weber function|next=Relation between Weber function and Struve function}}: 12.3.5
  494 bytes (70 words) - 04:16, 6 June 2016
• Relationship between Anger function and Weber function
  ...u}$ denotes an [[Anger function]] and $\mathbf{E}_{\nu}$ denotes a [[Weber function]]. ...gun|prev=Weber function|next=Relationship between Weber function and Anger function}}: 12.3.4
  456 bytes (65 words) - 04:15, 6 June 2016
• Relationship between Weber function 0 and Struve function 0
  ...f{E}_0$ denotes a [[Weber function]] and $\mathbf{H}_0$ denotes a [[Struve function]].
  249 bytes (32 words) - 13:18, 25 June 2016
• Relationship between Weber function 1 and Struve function 1
  ...f{E}_1$ denotes a [[Weber function]] and $\mathbf{H}_1$ denotes a [[Struve function]].
  263 bytes (34 words) - 13:19, 25 June 2016
• Relationship between Weber function and Struve function
  #REDIRECT [[Relationship between Weber function 0 and Struve function 0]]
  73 bytes (8 words) - 18:20, 28 June 2015
• 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
• 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
• 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
• 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
• Debye function
  275 bytes (42 words) - 15:56, 10 July 2017
• Incomplete beta function
  The incomplete beta function is defined by
  319 bytes (42 words) - 01:56, 23 December 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
• 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
• 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

Page text matches

• Lambert W
  The Lambert $W$ function is the (multi-valued) function that satisfies the equation ...om/watch?v=AJD8kh3DSAM 6: Recursion, Infinite Tetrations and the Lambert W Function (4 August 2014)]
  974 bytes (142 words) - 18:24, 16 June 2018
• Apéry's constant
  where $\zeta$ denotes the [[Riemann zeta function]]. This constant is notable because it is known in general that for integer
  682 bytes (105 words) - 17:17, 24 June 2016
• Prime counting
  The prime counting function $\pi \colon \mathbb{R} \rightarrow \mathbb{Z}^+$ is defined by the formula
  600 bytes (82 words) - 06:35, 22 June 2016
• Hermite (probabilist)
  ...a sequence of [[Orthogonal polynomial|orthogonal polynomials]] with weight function $e^{-\frac{x^2}{2}}$. <strong>Theorem:</strong> ([[Generating function]]) The Hermite polynomials obey
  2 KB (228 words) - 18:41, 24 May 2016
• Fransén–Robinson constant
  where $\dfrac{1}{\Gamma}$ denotes the [[reciprocal gamma function]].
  340 bytes (46 words) - 20:17, 20 June 2016
• Beta
  The beta function $B$ (note: $B$ is [https://en.wikipedia.org/wiki/Beta capital $\beta$] in G [[Partial derivative of beta function]]<br />
  3 KB (578 words) - 19:49, 15 March 2018
• Polylogarithm
  [https://www.youtube.com/watch?v=6v60ivoC2z8 polylogarithm function]
  646 bytes (91 words) - 20:28, 25 June 2017
• Cosine
  The cosine function, $\cos \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula where $e^z$ is the [[exponential function]].
  1 KB (177 words) - 22:09, 19 December 2017
• Euler-Mascheroni constant
  #the [[Barnes G]] function
  2 KB (206 words) - 20:57, 3 March 2018
• Book:Arthur Erdélyi/Higher Transcendental Functions Volume II
  ::::7.2.3. Kelvin's function and related functions
  5 KB (521 words) - 05:44, 4 March 2018
• Book:Edward Charles Titchmarsh/The Zeta-Function of Riemann
  {{Book|The Zeta-Function of Riemann|1930|Cambridge University Press||Edward Charles Titchmarch}} ...r primes|$(2')$]] (and [[Series for log(Riemann zeta) in terms of Mangoldt function|$(2')$]])
  1 KB (170 words) - 15:23, 18 March 2017
• Factorial
  [[Gamma function]]
  242 bytes (35 words) - 19:40, 9 October 2016
• Pochhammer
  ...ochhammer symbol $(a)_n$ is a notation that denotes the "rising factorial" function. It is defined by ...findme|next=findme}}: $18. (1)$ (note: Rainville calls this the "factorial function" and expresses it slightly differently by defining it by the equivalent for
  1 KB (187 words) - 23:25, 3 March 2018
• Mills' constant
  ...6/S0002-9904-1947-08849-2/S0002-9904-1947-08849-2.pdf A prime-representing function by W.H. Mills]
  323 bytes (52 words) - 19:00, 24 May 2016
• Tangent
  The tangent function is defined as the ratio of the [[sine]] and [[cosine]] functions:
  916 bytes (117 words) - 03:38, 6 July 2016
• Euler totient
  Euler's totient function $\phi \colon \{1,2,3,\ldots\} \rightarrow \{1,2,3,\ldots\}$ (not to be conf [https://www.youtube.com/watch?v=QbsWEVcjJy0 Euler's Phi Function] (6 October 2010)<br />
  2 KB (344 words) - 01:58, 21 December 2017
• Mobius function
  #REDIRECT [[Möbius function]]
  30 bytes (4 words) - 16:13, 4 October 2014
• Jacobi sn
  #$\mathrm{sn \hspace{2pt}}$ is an odd function
  815 bytes (121 words) - 19:06, 5 July 2016
• Jacobi cn
  #$\mathrm{cn \hspace{2pt}}$ is an even function
  762 bytes (111 words) - 19:06, 5 July 2016
• Mertens function
  Merten's function is defined by the formula where $\mu$ is the [[Möbius function]].
  129 bytes (22 words) - 16:13, 4 October 2014
• Möbius
  The Möbius function is the function $\mu$ defined by the formula [[Reciprocal of Riemann zeta as a sum of Möbius function for Re(z) greater than 1]]<br />
  2 KB (278 words) - 23:55, 8 December 2016
• Liouville lambda
  The Liouville function is defined by the formula where $\zeta$ denotes the [[Riemann zeta function]].
  1 KB (139 words) - 06:35, 22 June 2016
• Mangoldt
  The Mangoldt function is defined by the formula
  770 bytes (106 words) - 02:31, 28 November 2016
• Hurwitz zeta
  The Hurwitz zeta function is a generalization of the [[Riemann zeta]] function defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by [[Relationship between Hurwitz zeta and gamma function]]<br />
  575 bytes (76 words) - 01:27, 21 December 2016
• Laguerre L
  [[Generating function for Laguerre L]]<br /> ...ns for Scientists and Engineers|1968|W.W. Bell|prev=findme|next=Generating function for Laguerre L}}: $(6.3)$
  1 KB (180 words) - 14:37, 15 March 2018
• Euler E generating function
  where $e^{xt}$ denotes the [[exponential function]] and $E_n$ denotes an [[Euler E]] polynomial.
  519 bytes (75 words) - 01:05, 4 March 2018
• Gegenbauer C
  where $\left\lfloor \frac{n}{2} \right\rfloor$ denotes the [[floor]] function, $\Gamma$ denotes [[gamma]], and $k!$ denotes the [[factorial]].
  1 KB (181 words) - 01:29, 20 December 2017
• Jacobi P
  ...nomial $P_n^{(\alpha,\beta)}$ are [[orthogonal polynomials]] with [[weight function]] $w(x)=(1-x)^{\alpha}(1-x)^{\beta}$ on the interval $[-1,1]$ that obey $P_
  826 bytes (106 words) - 03:30, 11 June 2016
• Exponential integral E
  [[Relationship between the exponential integral and upper incomplete gamma function]]<br />
  1 KB (199 words) - 00:45, 24 March 2018
• Logarithmic integral
  [[Prime counting function]] <br />
  994 bytes (117 words) - 03:33, 17 March 2018
• Sine integral
  where $\mathrm{sinc}$ denotes the [[sinc]] function. ...Physics and Chemistry|1956|Ian N. Sneddon|prev=Cosine integral|next=Error function}}: $\S 5 (5.10)$
  1,012 bytes (130 words) - 00:42, 25 June 2017
• Bateman F
  where ${}_3F_2$ denotes the [[generalized hypergeometric function]]. The first few Bateman polynomials are
  1 KB (135 words) - 11:57, 10 October 2019
• Euler E
  [[Euler E generating function]]<br />
  754 bytes (117 words) - 01:05, 4 March 2018
• Catalan's constant
  ...stant can be expressed as $\beta(2)$ where $\beta$ is the [[Dirichlet beta function]].
  455 bytes (51 words) - 15:40, 25 February 2018
• Klein invariant J
  The Klein j-invariant $j(\tau)$ is ''the'' [[modular function]] which encodes arithmetic information about the [[singular moduli]] of [[i
  411 bytes (58 words) - 18:28, 24 May 2016
• Hermite (physicist)
  ...polynomials $H_n$ are a sequence of [[orthogonal polynomials]] with weight function $w(x)=e^{-x^2}$ over $(-\infty,\infty)$. [[Generating function for Hermite (physicist) polynomials]]<br />
  2 KB (256 words) - 00:49, 9 July 2016
• Dirichlet beta
  The Dirichlet $\beta$ function is defined by
  489 bytes (65 words) - 00:54, 11 December 2016
• Sinc
  ...athrm{sinc}$ function (sometimes called the "unnormalized" $\mathrm{sinc}$ function) is defined by It appears in the definition of the [[Sine integral]] function.
  1 KB (175 words) - 02:19, 16 September 2016
• Sum of divisors
  The sum of positive divisors function, $\sigma_x$, is defined by [[Sum of divisors functions written in terms of partition function]]<br />
  559 bytes (83 words) - 20:50, 26 June 2016
• Logarithm
  [[Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta]]<br />
  3 KB (452 words) - 05:03, 21 December 2017
• Polygamma
  The polygamma function of order $m$, $\psi^{(m)}(z)$, is defined by the formula ...mma]] function $\psi$ is the function $\psi^{(0)}(z)$ and the [[trigamma]] function is $\psi^{(1)}(z)$.
  2 KB (222 words) - 22:47, 17 March 2017
• Q-Polygamma function
  ...a functions of order $m$, $\psi_q^{(m)}$, are analogues of the [[polygamma function]] defined by ...ma_q(z).$ Here the function $\Gamma_q$ is the [[q-Gamma function|$q$-Gamma function]].
  368 bytes (60 words) - 18:56, 24 May 2016
• Polygamma functions
  #REDIRECT [[Polygamma function]]
  32 bytes (3 words) - 15:18, 14 October 2014
• Laplace transform
  ...tarrow \mathbb{C}$ be a function, then the Laplace transform of $f$ is the function defined by |Original function $f(t)$
  4 KB (583 words) - 03:37, 21 December 2017
• Arccos
  The function $\mathrm{arccos} \colon \mathbb{C} \setminus \{(-\infty,-1) \bigcup (1,\inf
  916 bytes (116 words) - 20:04, 22 November 2016
• Arcsin
  The function $\mathrm{arcsin} \colon \mathbb{C} \setminus \left\{ (-\infty,-1) \bigcup ( ...ub.uni-goettingen.de/dms/load/img/?PID=PPN600494829_0015%7CLOG_0028 On the function arc sin(x+iy)-Cayley]<br />
  1 KB (214 words) - 23:45, 22 December 2016
• Arctan
  The $\mathrm{arctan}$ function is the inverse function of the [[tangent]] function.<br />
  778 bytes (94 words) - 02:46, 16 September 2016
• Prime zeta P
  The prime zeta function is defined by [[Relationship between prime zeta, Möbius function, logarithm, and Riemann zeta]]<br />
  2 KB (248 words) - 23:29, 17 March 2017
• Arccot
  ...\right] \setminus \{0\}$ is the [[inverse function]] of the [[cotangent]] function.
  685 bytes (81 words) - 03:44, 6 July 2016
• Arcsec
  ...t\{ \dfrac{\pi}{2} \right\}$ is the [[inverse function]] of the [[secant]] function.
  526 bytes (62 words) - 03:44, 6 July 2016

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