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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.30.06.0070.01









  


  










Input Form





ArcSech[z]^2 == Subscript[F, Infinity][z] /; Subscript[F, n][z] == (1/4) Log[-(4/z^2)]^2 - ((Pi z)/2) Sqrt[-(1/z^2)] Log[-(4/z^2)] - Pi^2/4 - (z^2/4) (Log[-(4/z^2)] - Pi z Sqrt[-(1/z^2)]) Sum[(Pochhammer[3/2, k]/((k + 1)^2 k!)) z^(2 k), {k, 0, n}] + (z^4/16) Sum[(Pochhammer[3/2, k] z^(2 k))/((k + 1)^2 k!), {k, 0, n}]^2 == (-(z^(4 (2 + n))/(16 (2 + n)^4 (1 + n)!^2))) ((4 (2 + n)^2 ArcSec[z] (1 + n)!)/z^(2 (2 + n)) - 3 Pochhammer[5/2, n] HypergeometricPFQ[{1, 2 + n, 5/2 + n}, {3 + n, 3 + n}, 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





© 1998- Wolfram Research, Inc.