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ArcSinh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSinh[z] > Series representations > Generalized power series > Expansions at z==-i > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.25.06.0061.01









  


  








Input Form





ArcSinh[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == -((Pi I)/2) + Sqrt[2] I Sqrt[(-I) (z + I)] Sum[((-(I/2))^k Pochhammer[1/2, k] (z + I)^k)/((2 k + 1) k!), {k, 0, n}] == ArcSinh[z] - (((-I)^n 2^(3/2 + n) Gamma[3/2 + n]^2)/ (Pi (2 n + 3)!)) (z + I)^(1 + n) Sqrt[(-I) (z + I)] HypergeometricPFQ[{1, 3/2 + n, 3/2 + n}, {2 + n, 5/2 + n}, -(I ((z + I)/2))] && Element[n, Integers] && n >= 0








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)





2007-05-02