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ArcCsch




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving powers of the direct function and a power function





http://functions.wolfram.com/01.29.21.0031.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) ArcCsch[a z]^2, z] == (1/(2 a^2 (-1 + \[Alpha]) \[Alpha])) (z^(-2 + \[Alpha]) (2 a z ArcCsch[a z] (a z (-1 + \[Alpha]) ArcCsch[a z] + 2 Sqrt[1 + 1/(a^2 z^2)] Hypergeometric2F1[1, 1 - \[Alpha]/2, (3 - \[Alpha])/2, -(1/(a^2 z^2))]) + 2^\[Alpha] Sqrt[Pi] (-1 + \[Alpha]) Gamma[1 - \[Alpha]] HypergeometricPFQRegularized[ {1, 1 - \[Alpha]/2, 1 - \[Alpha]/2}, {(3 - \[Alpha])/2, 2 - \[Alpha]/2}, -(1/(a^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