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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Case of canceled double poles





http://functions.wolfram.com/07.23.06.0061.01









  


  








Input Form





Hypergeometric2F1[a, a + n, a - m, z] == (-1)^m ((Gamma[a - m] (m + n)!)/(Gamma[a] n!)) (-z)^(-a - n) Sum[(Pochhammer[a + n, k] Pochhammer[1 + m + n, k])/ (k! Pochhammer[1 + n, k])/z^k, {k, 0, Infinity}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0 && !IntervalMemberQ[Interval[{0, 1}], z]








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