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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Specific values > Specialized values > For fixed z and integer parameters





http://functions.wolfram.com/07.24.03.0169.01









  


  








Input Form





Hypergeometric2F1Regularized[1, n, m + 1/2, z] == (1/((n - 1) Gamma[m - 1/2])) Sum[Pochhammer[1/2 - n + m, k]/ (Pochhammer[2 - n, k] (1 - z)^(k + 1)), {k, 0, n - m - 1}] + ((Gamma[1/2 + n - m]/(Pi (n - 1)!)) (1 - z)^(m - n) (2 Sqrt[z/(1 - z)] ArcSin[Sqrt[z]] - Sum[((k - 1)! z^k)/Pochhammer[1/2, k], {k, 1, m - 1}]))/z^m /; Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0 && ((m = 1 && n > 2) || Inequality[1, Less, m, LessEqual, n])








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