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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Identities > Functional identities > Quadratic transformations with fixed a,b,z





http://functions.wolfram.com/07.24.17.0077.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, a + b - 1/2, z] == (1/Sqrt[1 - z]) Hypergeometric2F1Regularized[2 a - 1, 2 b - 1, a + b - 1/2, (1 - Sqrt[1 - z])/2]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a_", ",", "b_", ",", RowBox[List["a_", "+", "b_", "-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "a"]], "-", "1"]], ",", RowBox[List[RowBox[List["2", " ", "b"]], "-", "1"]], ",", RowBox[List["a", "+", "b", "-", FractionBox["1", "2"]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]]]]]], "]"]], SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]


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





2001-10-29