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ArcSech




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[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/01.30.21.0032.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) ArcSech[a z]^2, z] == (z^\[Alpha]/(2 \[Alpha])) (2 ArcSech[a z]^2 - (4/(a^2 z^2 (-2 + \[Alpha]) (-1 + \[Alpha]))) (Sqrt[(1 - a z)/(1 + a z)] (1 + a z) (-2 + \[Alpha]) ArcSech[a z] Hypergeometric2F1[1, 1 - \[Alpha]/2, (3 - \[Alpha])/2, 1/(a^2 z^2)] + HypergeometricPFQ[{1, 1 - \[Alpha]/2, 1 - \[Alpha]/2}, {3/2 - \[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