Inverse secant: Differentiation (formula 01.18.20.0004)

ArcSec

$Mathematica Notation$

Elementary Functions

ArcSec[z]

Differentiation

Fractional integro-differentiation

http://functions.wolfram.com/01.18.20.0004.01

Input Form

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

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