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• Error function is odd
  ...thrm{erf}$ denotes the [[error function]] (i.e. $\mathrm{erf}$ is an [[odd function]]). proving that $\mathrm{erf}$ is odd. $\blacksquare$
  800 bytes (116 words) - 03:41, 28 March 2017

Page text matches

• Book:Leonard Lewin/Dilogarithms and Associated Functions
  ::8. Legendre's Chi-function ::6. The Multiplication Formula for Odd Multiples
  4 KB (409 words) - 20:56, 27 June 2016
• 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
• Apéry's constant
  ...$\zeta(2n+1)$. Hence it became a notorious open problem to find $\zeta$ at odd integers.
  682 bytes (105 words) - 17:17, 24 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
• Jacobi sn
  #$\mathrm{sn \hspace{2pt}}$ is an odd function
  815 bytes (121 words) - 19:06, 5 July 2016
• Möbius
  The Möbius function is the function $\mu$ defined by the formula ...uarefree\hspace{2pt}positive\hspace{2pt}integer\hspace{2pt}with\hspace{2pt}odd\hspace{2pt}number\hspace{2pt}of\hspace{2pt}prime\hspace{2pt}factors} \\
  2 KB (278 words) - 23:55, 8 December 2016
• Sinh
  The hyperbolic sine function $\mathrm{sinh} \colon \mathbb{C} \rightarrow \mathbb{C}$ is defined by ...to-one]], its [[inverse function]] the [[arcsinh|inverse hyperbolic sine]] function is clear.
  2 KB (217 words) - 23:44, 21 October 2017
• Taylor series of sine
  where $\sin$ denotes the [[sine]] function. Using the [[Taylor series of the exponential function]] and the definition of $\sin$,
  1 KB (206 words) - 03:19, 1 July 2017
• Fresnel C
  The Fresnel C function is defined by the formula [[Fresnel C is odd]]<br />
  871 bytes (132 words) - 05:10, 21 December 2017
• Fresnel S
  The Fresnel $S$ function is defined by [[Fresnel S is odd]] <br />
  867 bytes (129 words) - 17:21, 5 October 2016
• Taylor series of cosine
  where $\cos$ denotes the [[cosine]] function. Using the [[Taylor series of the exponential function]] and the definition of $\cos$,
  1 KB (201 words) - 03:18, 1 July 2017
• Book:Earl David Rainville/Special Functions
  ::8. The Gamma function ::16. The Beta function
  7 KB (822 words) - 05:19, 21 December 2017
• Integral representation of Airy Ai
  The [[Airy Ai]] function ...force $f(t)e^{zt} \Bigg |_{C}=0$. We will do this by first determining the function $f$. Plugging this back into the formula $(*)$ yields
  5 KB (873 words) - 00:50, 13 September 2023
• Book:Milton Abramowitz/Handbook of mathematical functions
  ::4.1. Logarithmic Function ::4.2. Exponential Function
  22 KB (2,666 words) - 05:08, 21 December 2017
• Fibonacci numbers
  [[Sum of odd indexed Fibonacci numbers]]<br /> [[Fibonacci zeta function]]<br />
  2 KB (362 words) - 13:12, 1 August 2018
• Error function is odd
  ...thrm{erf}$ denotes the [[error function]] (i.e. $\mathrm{erf}$ is an [[odd function]]). proving that $\mathrm{erf}$ is odd. $\blacksquare$
  800 bytes (116 words) - 03:41, 28 March 2017
• Erf of conjugate is conjugate of erf
  where $\mathrm{erf}$ denotes the [[error function]] and $\overline{z}$ denotes the [[complex conjugate]]. ...ions|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
• Absolute convergence of secant zeta function
  The series defining the [[secant zeta function]] $\psi_s(z)$ converges absolutely in the following cases: # when $z=\dfrac{p}{q}$ with $q$ odd, $s>1$
  430 bytes (56 words) - 06:09, 16 June 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

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