Hyperbolic sine: Representations through more general functions (formula 01.19.26.0097)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Representations through more general functions

Through Meijer G

Classical cases involving parabolic cylinder function D

http://functions.wolfram.com/01.19.26.0097.01

Input Form

Sinh[z^2] (ParabolicCylinderD[\[Nu], 2 z] - ParabolicCylinderD[\[Nu], -2 z]) == (Pi^(3/2)/(2^((1 + \[Nu])/2) Gamma[-\[Nu]])) MeijerG[{{1 + \[Nu]/2}, {1/4}}, {{1/2}, {0, 1/4}}, 2 z^2] - 2^(\[Nu]/2) Sin[(Pi \[Nu])/2] MeijerG[{{(1 - \[Nu])/2}, {}}, {{1/2}, {0}}, 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