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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Identities > Functional identities > Quadratic transformations with fixed a,c,z





http://functions.wolfram.com/07.23.17.0114.01









  


  








Input Form





Hypergeometric2F1[a, a + 1/2, c, z] == Hypergeometric2F1[2 a, 2 c - 2 a - 1, c, (Sqrt[1 - z] - 1)/(2 Sqrt[1 - z])]/ (1 - z)^a








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", RowBox[List["a_", "+", FractionBox["1", "2"]]], ",", "c_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["-", "a"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["2", " ", "a"]], ",", RowBox[List[RowBox[List["2", " ", "c"]], "-", RowBox[List["2", " ", "a"]], "-", "1"]], ",", "c", ",", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "-", "1"]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]]]]]]


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





2001-10-29