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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 simple poles





http://functions.wolfram.com/07.24.06.0022.01









  


  










Input Form





Hypergeometric2F1Regularized[a, b, c, z] == (Pi/Sin[Pi (b - a)]) (((1/(Gamma[b] Gamma[c - a])) Sum[(Pochhammer[a, k] Pochhammer[a - c + 1, k])/ (k! Gamma[a - b + 1 + k])/z^k, {k, 0, Infinity}])/(-z)^a - ((1/(Gamma[a] Gamma[c - b])) Sum[(Pochhammer[b, k] Pochhammer[b - c + 1, k])/ (k! Gamma[b - a + 1 + k])/z^k, {k, 0, Infinity}])/(-z)^b) /; Abs[z] > 1 && !Element[a - b, 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)





2001-10-29





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