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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 b, z





http://functions.wolfram.com/07.24.03.0161.01









  


  








Input Form





Hypergeometric2F1Regularized[1, b, 3/2, z] == ((2^(3/2 - b) Gamma[1 - b])/(Pi Sqrt[z])) (1 - z)^((1 - 2 b)/4) LegendreQ[1/2 - b, b - 1/2, 2, Sqrt[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["1", ",", "b_", ",", FractionBox["3", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["3", "2"], "-", "b"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "b"]]]], ")"]]]]], " ", RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", "b"]], ",", RowBox[List["b", "-", FractionBox["1", "2"]]], ",", "2", ",", SqrtBox["z"]]], "]"]]]], RowBox[List["\[Pi]", " ", SqrtBox["z"]]]]]]]]


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





2001-10-29