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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/07.24.26.0260.01









  


  










Input Form





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