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ArcCosh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Series representations > Generalized power series > Expansions at z==1 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.26.06.0081.01









  


  








Input Form





ArcCosh[z]^2 == Subscript[F, Infinity][z] /; Subscript[F, n][z] == 2 (z - 1) Sum[(Pochhammer[1/2, k] (1 - z)^k)/(2^k (2 k + 1) k!), {k, 0, n}]^2 == ArcCosh[z]^2 + ((2^(1/2 - n) Gamma[3/2 + n])/((3 + 2 n) Sqrt[Pi] (n + 1)!)) (1 - z)^(3/2 + n) ArcCos[z] HypergeometricPFQ[ {1, 3/2 + n, 3/2 + n}, {2 + n, 5/2 + n}, (1 - z)/2] - ((2^(-1 - 2 n) Gamma[3/2 + n]^2)/((3 + 2 n)^2 Pi (n + 1)!^2)) (1 - z)^(3 + 2 n) HypergeometricPFQ[{1, 3/2 + n, 3/2 + n}, {2 + n, 5/2 + n}, (1 - z)/2]^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