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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




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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