Hyperbolic cosine integral: Representations through more general functions (formula 01.20.26.0103)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Representations through more general functions

Through Meijer G

Classical cases involving exp and Hermite H

http://functions.wolfram.com/01.20.26.0103.01

Input Form

(Cosh[z^2] (HermiteH[\[Nu], Sqrt[2] z] + HermiteH[\[Nu], (-Sqrt[2]) z]))/ E^z^2 == (Pi^(3/2)/(Sqrt[2] Gamma[-\[Nu]])) MeijerG[{{1 + \[Nu]/2}, {1/4}}, {{0}, {1/2, 1/4}}, 2 z^2] + 2^\[Nu] Cos[(Pi \[Nu])/2] MeijerG[{{(1 - \[Nu])/2}, {}}, {{0}, {1/2}}, 2 z^2] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/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