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variants of this functions
Hypergeometric2F1






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





http://functions.wolfram.com/07.23.06.0031.01









  


  










Input Form





Hypergeometric2F1[a, a + n, a + m, z] == (((Gamma[a + m] Gamma[n])/(Gamma[m] Gamma[a + n])) Sum[(Pochhammer[a, k] Pochhammer[1 - m, k])/(k! Pochhammer[1 - n, k])/ z^k, {k, 0, m - 1}])/(-z)^a + ((Pochhammer[a, m] (n - m)!)/n!) (-1)^m (-z)^(-a - n) Hypergeometric2F1[a + n, 1 - m + n, 1 + n, 1/z] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0 && m <= n && !IntervalMemberQ[Interval[{0, 1}], z]










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





© 1998- Wolfram Research, Inc.