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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Case of double poles





http://functions.wolfram.com/07.24.06.0065.01









  


  










Input Form





Hypergeometric2F1Regularized[a, a + n, c, z] == Subscript[F, Infinity][z, a, a + n, c] /; (Subscript[F, n][z, a, a + n, c] == ((-z)^(-a - n)/(Gamma[a + n] Gamma[c - a])) Sum[(((Pochhammer[a, k + n] Pochhammer[1 + a - c, k + n])/ (k! (k + n)!)) (PolyGamma[k + n + 1] + PolyGamma[k + 1] - PolyGamma[a + n + k] - PolyGamma[c - a - n - k] + Log[-z]))/z^k, {k, 0, m}] + (1/((-z)^a Gamma[a + n])) Sum[(Pochhammer[a, k] Gamma[n - k])/(k! Gamma[c - a - k])/z^k, {k, 0, n - 1}] == Hypergeometric2F1Regularized[a, a + n, c, z] - ((-1)^n/(Gamma[a] Gamma[a + n])) MeijerG[{{-a - m - n, -a - m - n}, {1 - a, 1 - a - n}}, {{0, -a - n - m, -a - n - m}, {1 - c}}, -z] && Element[m, Integers] && m >= 0) && Element[n, Integers] && n >= 0 && !Element[c - a, Integers]










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





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