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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/07.23.26.0262.01









  


  










Input Form





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