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• Bernoulli-Euler Gamma function
  ....de/math/factorial/hadamard/HadamardsGammaFunctionMJ.html#id1 Is the Gamma function misdefined?]
  128 bytes (16 words) - 22:45, 13 January 2015
• Heaviside step function
  The Heaviside step function is
  148 bytes (22 words) - 18:32, 24 May 2016
• Sinc function
  18 bytes (2 words) - 04:41, 19 January 2015
• Beta function
  18 bytes (2 words) - 06:53, 19 January 2015
• Dedekind eta function
  26 bytes (3 words) - 07:08, 19 January 2015
• Digamma function
  21 bytes (2 words) - 07:08, 19 January 2015
• Exponential function
  25 bytes (2 words) - 07:15, 19 January 2015
• Gamma function
  19 bytes (2 words) - 07:21, 19 January 2015
• Generalized hypergeometric function
  31 bytes (3 words) - 07:30, 19 January 2015
• Thomae function
  Thomae's function (sometimes called the popcorn function, raindrop function, Stars over Babylon) is given by the formula File:Thomae.png|Plot of the Thomae function.
  1 KB (150 words) - 00:36, 9 December 2016
• Polygamma function
  23 bytes (2 words) - 07:52, 19 January 2015
• Reciprocal gamma function
  30 bytes (3 words) - 07:56, 19 January 2015
• Lambert W function
  23 bytes (3 words) - 08:01, 19 January 2015
• Dirichlet beta function
  28 bytes (3 words) - 08:11, 19 January 2015
• Dirichlet eta function
  27 bytes (3 words) - 08:14, 19 January 2015
• Hadamard's gamma function
  28 bytes (3 words) - 08:17, 19 January 2015
• Minkowski question mark function
  37 bytes (4 words) - 08:25, 19 January 2015
• Partition function
  23 bytes (2 words) - 08:30, 19 January 2015
• Riemann xi function
  24 bytes (3 words) - 08:35, 19 January 2015
• Planck's radiation function
  30 bytes (3 words) - 08:42, 19 January 2015
• Q-Gamma function
  21 bytes (2 words) - 10:12, 19 January 2015
• Q-Binomial function
  24 bytes (2 words) - 10:47, 19 January 2015
• Hurwitz zeta function
  26 bytes (3 words) - 11:25, 19 January 2015
• Prime zeta function
  26 bytes (4 words) - 11:42, 19 January 2015
• Mangoldt function
  22 bytes (2 words) - 11:48, 19 January 2015
• Möbius function
  21 bytes (3 words) - 06:35, 22 June 2016
• Sum of positive divisors function
  29 bytes (4 words) - 11:56, 19 January 2015
• Prime counting function
  28 bytes (3 words) - 12:00, 19 January 2015
• Liouville function
  30 bytes (3 words) - 12:09, 19 January 2015
• Bessel function
  20 bytes (2 words) - 01:31, 17 March 2015
• Secant zeta function
  [[Absolute convergence of secant zeta function]]
  295 bytes (40 words) - 06:10, 16 June 2016
• Cotangent zeta function
  200 bytes (30 words) - 06:48, 16 June 2016
• Struve function
  [[Relationship between Struve function and hypergeometric pFq]]<br /> [[Relationship between Weber function 0 and Struve function 0]]<br />
  1 KB (218 words) - 01:09, 21 December 2017
• Error function
  The (normalized) error function $\mathrm{erf}$ is defined by where $\pi$ denotes [[pi]] and $e^{-\tau^2}$ denotes the [[exponential]] function.
  2 KB (271 words) - 00:43, 25 June 2017
• Closed form for partition function with sinh
  a [[sawtooth function]], define where $p$ denotes the [[partition]] function, $\pi$ denotes [[pi]], and $\sinh$ denotes the [[sinh|hyperbolic sine]].
  1 KB (172 words) - 20:40, 26 June 2016
• Pure recurrence relation for partition function
  ...the [[partition]] function and $\sigma_1$ denotes the [[sum of divisors]] function. ...rm for partition function with sinh|next=Recurrence relation for partition function with sum of divisors}}: $24.2.1 \mathrm{II}.A.$
  581 bytes (80 words) - 20:41, 26 June 2016
• Ihara zeta function
  Let $X$ be a finite [[graph]]. The Ihara zeta function is given by the formula ...an analogue of the [[Euler product]] representation of the [[Riemann zeta function]].
  765 bytes (122 words) - 18:52, 24 May 2016
• Cosine function
  20 bytes (2 words) - 15:52, 4 October 2014
• 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
• Q-Beta function
  272 bytes (50 words) - 18:54, 24 May 2016
• Sine function
  18 bytes (2 words) - 15:52, 4 October 2014
• Tangent function
  21 bytes (2 words) - 15:53, 4 October 2014
• Mobius function
  #REDIRECT [[Möbius function]]
  30 bytes (4 words) - 16:13, 4 October 2014
• 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
• 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
• 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
• Q-theta function
  235 bytes (39 words) - 00:56, 19 October 2014
• Riemann zeta function
  26 bytes (3 words) - 19:40, 9 June 2016
• Dedekind zeta function
  ...finite [[field extension]] of the [[rational numbers]]. The Dedekind zeta function of $F$ is
  896 bytes (130 words) - 18:52, 24 May 2016
• Dirichlet L-function
  Let $\chi$ be a [[Dirichlet character]]. The Dirichlet $L$-function associated with $\chi$ is ...ac.uk/people/staff/mrwatkin//zeta/devlin.pdf How Euler discovered the zeta function]
  379 bytes (58 words) - 19:27, 17 November 2016

Page text matches

• Main Page
  <div class="grid"><center>[[Identity function|<randomimagebycategory categories="identityglyph" width="45" />]]<br /> [[Identity function|Identity]]</center></div>
  26 KB (2,938 words) - 15:47, 26 August 2023
• Hypergeometric pFq
  The generalized hypergeometric function ${}_pF_q$ is defined by
  2 KB (274 words) - 14:42, 15 March 2018
• Series for log(riemann zeta) over primes
  ...ct for Riemann zeta|next=Series for log(Riemann zeta) in terms of Mangoldt function}}: § Introduction $(2')$
  532 bytes (68 words) - 03:09, 1 July 2017
• Hypergeometric 0F0
  The hypergeometric ${}_0F_0$ function is defined by the series It is a special case of the [[hypergeometric pFq]] function.
  328 bytes (43 words) - 06:04, 10 January 2017
• Bernoulli-Euler Gamma function
  ....de/math/factorial/hadamard/HadamardsGammaFunctionMJ.html#id1 Is the Gamma function misdefined?]
  128 bytes (16 words) - 22:45, 13 January 2015
• Hadamard gamma
  The Hadamard gamma function is defined by the formula where $\Gamma$ denotes the [[gamma function]].
  2 KB (267 words) - 18:28, 24 May 2016
• Spherical Bessel j
  The spherical Bessel function of the first kind is defined by where $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
  480 bytes (66 words) - 22:44, 20 June 2016
• Spherical Bessel y
  The spherical Bessel function of the second kind is where $Y_{\nu}$ denotes the [[Bessel Y sub nu|Bessel function of the second kind]].
  466 bytes (63 words) - 01:14, 18 July 2016
• Q-Gaussian distribution
  The $q$-Gaussian distribution has [[probability density function]]
  498 bytes (74 words) - 18:55, 24 May 2016
• Heaviside step function
  The Heaviside step function is
  148 bytes (22 words) - 18:32, 24 May 2016
• Hankel H (1)
  ...function of the first kind]] and $Y_{\nu}$ is the [[Bessel Y sub nu|Bessel function of the second kind]]. Note the similarity of these functions to the [[Hanke
  953 bytes (142 words) - 23:59, 22 December 2016
• Hankel H (2)
  ...Bessel function of the first kind]] and $Y_{\nu}$ is the [[Bessel Y|Bessel function of the second kind]]. Note the similarity of these functions to the [[Hanke
  809 bytes (127 words) - 23:58, 22 December 2016
• Modified Bessel I
  The modified Bessel function of the first kind is defined by ...notes the [[imaginary number]] and $J_{\nu}$ denotes the [[Bessel J|Bessel function of the first kind]].
  954 bytes (145 words) - 23:53, 10 June 2016
• Modified Bessel K
  The modified Bessel function of the second kind is defined by where $I_{\nu}$ is the [[Modified Bessel I sub nu|modified Bessel function of the first kind]].
  775 bytes (110 words) - 23:46, 10 June 2016
• Difference equation of hypergeometric type
  where the function $\rho$ satisfies a [[Pearson difference equation]]
  862 bytes (126 words) - 08:58, 17 January 2015
• Dawson D-
  The Dawson function $D-$ is defined by [[Error function]]<br />
  289 bytes (41 words) - 00:12, 29 October 2017
• Dawson D+
  The Dawson function $D+$ (sometimes called the Dawson $F$ function) is defined by [[Error function]]<br />
  437 bytes (60 words) - 00:21, 29 October 2017
• Böhmer C
  The Böhmer $C$ function is defined by
  334 bytes (48 words) - 06:51, 10 January 2017
• Thomae function
  Thomae's function (sometimes called the popcorn function, raindrop function, Stars over Babylon) is given by the formula File:Thomae.png|Plot of the Thomae function.
  1 KB (150 words) - 00:36, 9 December 2016
• Devil's staircase
  The Devil's staircase (also known as the Cantor function) is a function $c \colon [0,1] \rightarrow [0,1]$ can be expressed by the following rules: File:Cantor function.gif|Construction of $c$ in steps.
  1 KB (146 words) - 16:03, 10 July 2017
• Full list
  <td><center>[[File:erfthumb.png|45px|link=Error function]]<br /> [[Error function]]</center></td>
  12 KB (1,622 words) - 00:11, 5 May 2015
• Upper incomplete gamma
  The upper incomplete gamma function $\Gamma$ is defined by [[:Relationship between the exponential integral and upper incomplete gamma function]]
  262 bytes (35 words) - 03:22, 1 July 2017
• Sum of reciprocal Pochhammer symbols of a fixed exponent
  ...k)_p$ denotes the [[Pochhammer]] symbol and $\Gamma$ denotes the [[gamma]] function.
  318 bytes (44 words) - 12:40, 17 September 2016
• Beta in terms of sine and cosine
  ...], $\sin$ denotes the [[sine]] function, and $\cos$ denotes the [[cosine]] function.
  1 KB (223 words) - 21:04, 3 March 2018
• Beta in terms of gamma
  where $B$ denotes the [[beta]] function and $\Gamma$ denotes the [[gamma]] function.
  422 bytes (57 words) - 15:10, 6 October 2016
• Taylor series
  A Taylor series is a way to express a function as an infinite series under suitable differentiability conditions. The Tayl [[Taylor series of the exponential function]]<br />
  438 bytes (66 words) - 03:48, 6 June 2016
• Weierstrass factorization theorem
  ...a zero of order $0$ means that $f(0) \neq 0$). Then there exists an entire function $g$ and a sequence of integers $\{p_n\}$ such that [[Gamma function Weierstrass product]]<br />
  923 bytes (136 words) - 19:12, 26 November 2016
• Riemann-Landau xi
  The Riemann-Landau $\Xi$ function is defined by * {{BookReference|The Zeta-Function of Riemann|1930|Edward Charles Titchmarsh|prev=Functional equation for Riem
  403 bytes (49 words) - 15:28, 18 March 2017
• Signum
  ...\mathbb{R} \rightarrow \{-1,0,1\}$ (also called the sign function) is the function The function is occasionally extended to a function $\mathrm{sgn} \colon \mathbb{C} \rightarrow \mathbb{C}$ by
  999 bytes (131 words) - 05:12, 11 February 2018
• Legendre's constant
  where $\log$ denotes the [[logarithm]] and $\pi$ denotes the [[prime counting function]].
  615 bytes (88 words) - 18:59, 24 May 2016
• Logarithmically convex
  ...$f$ is called logarithmically convex (sometimes called superconvex) if the function $g(x)=\log f(x)$ is [[convex]].
  126 bytes (20 words) - 04:14, 20 March 2015
• Mertens
  Let $n \in \mathbb{Z}^+$. Define the Mertens function where $\mu$ is the [[Möbius function]].
  555 bytes (78 words) - 17:41, 12 October 2016
• Secant zeta function
  [[Absolute convergence of secant zeta function]]
  295 bytes (40 words) - 06:10, 16 June 2016
• Book:Leonard Lewin/Dilogarithms and Associated Functions
  ::8. Legendre's Chi-function ::8. Function Equations Involving Several Variables
  4 KB (409 words) - 20:56, 27 June 2016
• Hyperfactorial
  [[Hyperfactorial in terms of K-function]]<br />
  426 bytes (58 words) - 19:39, 25 September 2016
• Struve function
  [[Relationship between Struve function and hypergeometric pFq]]<br /> [[Relationship between Weber function 0 and Struve function 0]]<br />
  1 KB (218 words) - 01:09, 21 December 2017
• Elliptic K
  The elliptic $K$ function (also known as the complete elliptic integral of the first kind) is defined
  635 bytes (84 words) - 04:48, 21 December 2017
• Gamma
  ...lon \mathbb{C} \setminus \{0,-1,-2,\ldots\} \rightarrow \mathbb{C}$ is the function initially defined for $\mathrm{Re}(z)>0$ by the integral by the formula The [[analytic continuation]] of $\Gamma$ leads to a [[meromorphic function]] with [[pole | poles]] at the negative integers.
  5 KB (678 words) - 18:12, 16 June 2018
• Riemann zeta
  The Riemann zeta function $\zeta$ is defined for $\mathrm{Re}(z)>1$ by [[Laurent series of the Riemann zeta function]]<br />
  3 KB (417 words) - 18:40, 12 May 2017
• Q-Gamma
  Let $0<q<1$. Define the $q$-gamma function by the formula ...The function $\Gamma_q$ is a [[q-analogue | $q$-analogue]] of the [[gamma function]].
  2 KB (252 words) - 00:13, 30 May 2017
• Error function
  The (normalized) error function $\mathrm{erf}$ is defined by where $\pi$ denotes [[pi]] and $e^{-\tau^2}$ denotes the [[exponential]] function.
  2 KB (271 words) - 00:43, 25 June 2017
• Sine
  The sine function $\sin \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by ...-theory-fall-2006/projects/chan.pdf The sine product formula and the gamma function]<br />
  2 KB (207 words) - 17:34, 1 July 2017
• Partition
  The partition function $p \colon \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ is defined so that $p(n)$ [[Generating function for partition function]]<br />
  820 bytes (109 words) - 20:50, 26 June 2016
• Format notes
  =Defining a new function= The such-and-such function $\mathrm{mathname} \colon domain \rightarrow codomain$ is defined by
  8 KB (1,248 words) - 04:48, 26 November 2016
• Q-Binomial
  The $q$-Binomial function is
  1 KB (203 words) - 18:56, 24 May 2016
• Closed form for partition function with sinh
  a [[sawtooth function]], define where $p$ denotes the [[partition]] function, $\pi$ denotes [[pi]], and $\sinh$ denotes the [[sinh|hyperbolic sine]].
  1 KB (172 words) - 20:40, 26 June 2016
• Pure recurrence relation for partition function
  ...the [[partition]] function and $\sigma_1$ denotes the [[sum of divisors]] function. ...rm for partition function with sinh|next=Recurrence relation for partition function with sum of divisors}}: $24.2.1 \mathrm{II}.A.$
  581 bytes (80 words) - 20:41, 26 June 2016
• Ihara zeta function
  Let $X$ be a finite [[graph]]. The Ihara zeta function is given by the formula ...an analogue of the [[Euler product]] representation of the [[Riemann zeta function]].
  765 bytes (122 words) - 18:52, 24 May 2016
• Exponential
  The exponential function $\exp \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by the formula [[Derivative of the exponential function]]<br />
  2 KB (327 words) - 23:37, 21 October 2017
• Airy Bi
  The Airy function $\mathrm{Bi}$ (sometimes called the "Bairy function") is a solution of the [[Airy differential equation]] which is [[linearly independent]] from the [[Airy Ai]] function.
  2 KB (216 words) - 16:07, 21 October 2017

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