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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/07.24.26.0203.01









  


  








Input Form





(Sqrt[z] + Sqrt[1 + z])^(a + b - c) Hypergeometric2F1Regularized[a, b, c, (Sqrt[z] - Sqrt[1 + z])/(2 Sqrt[z])] Hypergeometric2F1[-a + c, -b + c, 1 - a - b + c, (Sqrt[z] - Sqrt[1 + z])/(2 Sqrt[z])] == ((2^(-1 + c) Gamma[1 - a - b + c])/(Sqrt[Pi] Gamma[-a + c] Gamma[-b + c])) MeijerG[{{1 + (a + b - c)/2}, {(3 c - a - b)/2, (a + b + c)/2, (c - a - b)/2 + 1}}, {{(-a + b + c)/2, (a - b + c)/2, c/2, (1 + c)/2}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]








Standard Form





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MathML Form







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</mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29