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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Representations through more general functions > Through Meijer G > Classical cases involving products of 2F~1 with algebraic arguments





http://functions.wolfram.com/07.24.26.0137.01









  


  








Input Form





(Sqrt[z] + Sqrt[1 + z])^(3/2 + 2 a - 2 c) Hypergeometric2F1Regularized[a, 1/2 + a, c, (Sqrt[z] - Sqrt[1 + z])/(2 Sqrt[z])] Hypergeometric2F1Regularized[1 - a, 1/2 - a, 1/2 - 2 a + c, (Sqrt[z] - Sqrt[1 + z])/(2 Sqrt[z])] == (4^(-a + c - 1)/(Pi Gamma[-1 - 2 a + 2 c])) MeijerG[{{7/4 + a - c}, {3/4 + a, 1/4 + c - a, 5/4 - a}}, {{1/4, 1/2, 3/4, 1}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], 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