Search results

Create the page "Function" on this wiki! See also the search results found.

Page title matches

• 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
• 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

• 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
• 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

View (previous 100 | next 100) (20 | 50 | 100 | 250 | 500)