Hyperbolic sine integral: Integration (formula 06.39.21.0076)

SinhIntegral

$Mathematica Notation$

Involving the direct function

http://functions.wolfram.com/06.39.21.0076.01

Input Form

Integrate[(t^(\[Alpha] - 1) SinhIntegral[t])/E^(z t), {t, 0, Infinity}] == z^(-1 - \[Alpha]) Gamma[1 + \[Alpha]] HypergeometricPFQ[ {1/2, (1 + \[Alpha])/2, 1 + \[Alpha]/2}, {3/2, 3/2}, 1/z^2] /; Re[z] > 1 && Re[\[Alpha]] > -1

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