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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==1 > For the function itself > Logarithmic cases





http://functions.wolfram.com/07.23.06.0012.01









  


  








Input Form





Hypergeometric2F1[a, b, a + b, z] == (Gamma[a + b]/(Gamma[a] Gamma[b])) Sum[((Pochhammer[a, k] Pochhammer[b, k])/k!^2) (-Log[1 - z] + 2 PolyGamma[k + 1] - PolyGamma[a + k] - PolyGamma[b + k]) (1 - z)^k, {k, 0, Infinity}] /; Abs[1 - z] < 1








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