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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Representations through more general functions > Through Meijer G > Generalized cases involving algebraic functions and 2F~1with algebraic arguments





http://functions.wolfram.com/07.23.26.0263.01









  


  










Input Form





(z + Sqrt[1 + z^2])^(1/2 + 2 a - c) Hypergeometric2F1[a, 1/2 + a, c, (z - Sqrt[1 + z^2])/(2 z)] Hypergeometric2F1Regularized[-(1/2) - a + c, -a + c, 1/2 - 2 a + c, (z - Sqrt[1 + z^2])/(2 z)] == ((2^(-3 - 2 a + 3 c) Gamma[c])/(Pi Gamma[-1 - 2 a + 2 c])) MeijerG[{{(5 - 2 c)/4 + a}, {(1 + 2 c)/4 + a, (6 c - 1)/4 - a, (1/4) (3 + 2 c) - a}}, {{(1/4) (-1 + 2 c), c/2, (1/4) (1 + 2 c), (1 + c)/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





© 1998-2014 Wolfram Research, Inc.