Hyperbolic cosine integral: Representations through more general functions (formula 01.20.26.0127)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Representations through more general functions

Through Meijer G

Generalized cases involving parabolic cylinder function D

http://functions.wolfram.com/01.20.26.0127.01

Input Form

Cosh[z^2] ParabolicCylinderD[\[Nu], -2 z] == (Pi^(3/2)/(2^((1 + \[Nu])/2) Gamma[-\[Nu]])) MeijerG[{{1 + \[Nu]/2}, {1/8, 5/8}}, {{0, 1/2}, {1/8, 5/8}}, Sqrt[2] z, 1/2] + 2^(\[Nu]/2 - 1) MeijerG[{{(1 - \[Nu])/2}, {(1 + \[Nu])/2}}, {{0, 1/2}, {(1 + \[Nu])/2}}, Sqrt[2] z, 1/2]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02