Inverse hyperbolic secant : Representations through more general functions (formula 01.30.26.0028)

ArcSech

$Mathematica Notation$

Elementary Functions

ArcSech[z]

Representations through more general functions

Through Meijer G

Classical cases for the direct function itself

http://functions.wolfram.com/01.30.26.0028.01

Input Form

ArcSech[Sqrt[z]] - (Pi Sqrt[1/z - 1])/(2 Sqrt[1 - 1/z]) + ((Sqrt[1/z] Log[-4/z])/(2 Sqrt[-z^(-1)])) (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) - (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) (Sqrt[1/z]/(2 Sqrt[-z^(-1)])) Sum[(Pochhammer[1/2, k] z^k)/(k k!), {k, 1, n}] == (((-1)^(-1 + n) Sqrt[1/z])/(2 Sqrt[Pi] Sqrt[-z^(-1)])) (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) MeijerG[{{1/2, 1, 1 + n}, {}}, {{1 + n}, {0, 0}}, -z] /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{-Infinity, 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)

2003-08-21