Hyperbolic sine: Representations through more general functions (formula 01.19.26.0021)

Sinh

$Mathematica Notation$

Elementary Functions

Sinh[z]

Representations through more general functions

Through Meijer G

Classical cases involving coth^-1 in the arguments and sgn

http://functions.wolfram.com/01.19.26.0021.01

Input Form

((1 - z) Sign[1 - Abs[z]])^\[Nu] Sinh[\[Nu] ArcCoth[(1 + z)/(2 Sqrt[z])]] == (-(Sqrt[Pi]/Gamma[-\[Nu]])) Gamma[1/2 + \[Nu]] MeijerG[{{1/2 + \[Nu]}, {1 + \[Nu]}}, {{1/2}, {0}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]

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)

2001-10-29