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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/07.24.06.0025.01









  


  










Input Form





Hypergeometric2F1Regularized[a, a + n, c, z] == ((-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]))/z^k, {k, 0, Infinity}] + (Sin[(c - a) Pi]/(Pi n! Gamma[a])) Gamma[1 + a - c + n] Log[-z] (-z)^(-a - n) Hypergeometric2F1[a + n, 1 + a - c + n, 1 + n, 1/z] + ((1/Gamma[a + n]) Sum[(Pochhammer[a, k] Gamma[n - k])/ (k! Gamma[c - a - k])/z^k, {k, 0, n - 1}])/(-z)^a /; Abs[z] > 1 && Element[n, Integers] && n >= 0 && !Element[c - a, Integers]










Standard Form





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MathML Form







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</apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998-2014 Wolfram Research, Inc.