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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 > Generalized cases involving algebraic functions and 2F1with algebraic arguments





http://functions.wolfram.com/07.24.26.0268.01









  


  








Input Form





(Hypergeometric2F1Regularized[a, b, 1 + a - b, (-z + Sqrt[1 + z^2])/ (z + Sqrt[1 + z^2])] Hypergeometric2F1[a, b, 1 + a - b, (-z + Sqrt[1 + z^2])/(z + Sqrt[1 + z^2])])/(z + Sqrt[1 + z^2])^(2 a) == (Gamma[1 + a - b]/(4^b (Sqrt[Pi] Gamma[a] Gamma[1 + a - 2 b]))) MeijerG[{{1 - a}, {1 - b, 1 + a - 2 b}}, {{0, 1 - 2 b, 1/2 - b}, {}}, z, 1/2] /; Re[z] > 0








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