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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/07.24.26.0266.01









  


  








Input Form





(z + Sqrt[1 + z^2])^(1 - c) Hypergeometric2F1Regularized[a, 1 - a, c, (z - Sqrt[1 + z^2])/(2 z)] Hypergeometric2F1[2 - a - c, 1 + a - c, 2 - c, (z - Sqrt[1 + z^2])/(2 z)] == ((2^(1 - c) Sin[a Pi] Gamma[2 - c])/ Pi^(3/2)) MeijerG[{{(3 - c)/2}, {(5 - 3 c)/2, (1 + c)/2}}, {{1 - c/2, (3 - c)/2 - a, (1 - c)/2 + a}, {}}, z, 1/2] /; !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