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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/07.24.06.0026.01









  


  










Input Form





Hypergeometric2F1Regularized[a, a + n, c, z] \[Proportional] (((n - 1)!/(Gamma[a + n] Gamma[c - a])) (1 + O[1/z]))/(-z)^a + (Sin[(c - a) Pi]/(Pi n! Gamma[a])) Gamma[1 + a - c + n] (-z)^(-a - n) (Log[-z] - EulerGamma - PolyGamma[c - a - n] + PolyGamma[1 + n] - PolyGamma[a + n]) (1 + O[1/z]) /; (Abs[z] -> Infinity) && 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)





2001-10-29





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