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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 algebraic functions and 2F1with algebraic arguments





http://functions.wolfram.com/07.24.26.0196.01









  


  








Input Form





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