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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/07.24.26.0209.01









  


  








Input Form





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