Inverse hyperbolic secant : Differentiation (formula 01.30.20.0004)

ArcSech

$Mathematica Notation$

Elementary Functions

ArcSech[z]

Differentiation

Fractional integro-differentiation

http://functions.wolfram.com/01.30.20.0004.01

Input Form

D[ArcSech[z], {z, \[Alpha]}] == (1/(z^\[Alpha] (2 Gamma[1 - \[Alpha]]))) (2 EulerGamma + Log[-(4/z^2)] + 2 PolyGamma[1 - \[Alpha]]) - ((Pi z^(1 - \[Alpha]))/(2 Gamma[1 - \[Alpha]])) Sqrt[-(1/z^2)] - 2^(\[Alpha] - 3) Sqrt[Pi] z^(2 - \[Alpha]) HypergeometricPFQRegularized[ {1, 1, 3/2, 3/2}, {2, 3/2 - \[Alpha]/2, 2 - \[Alpha]/2}, z^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)

2001-10-29