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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Specific values > Specialized values > For fixed a, b, z





http://functions.wolfram.com/07.24.03.0082.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, a + b - 1/2, z] == 2^(a + b - 3/2) (1/Sqrt[1 - z]) z^((3 - 2 a - 2 b)/4) LegendreP[-a + b - 1/2, 3/2 - a - b, 2, Sqrt[1 - z]]








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[SuperscriptBox["2", RowBox[List["a", "+", "b", "-", FractionBox["3", "2"]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "a"]], "-", RowBox[List["2", " ", "b"]]]], ")"]]]]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "+", "b", "-", FractionBox["1", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", "a", "-", "b"]], ",", "2", ",", SqrtBox[RowBox[List["1", "-", "z"]]]]], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]


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





2001-10-29