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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > Specialized values > For fixed a, b, z





http://functions.wolfram.com/07.23.03.0103.01









  


  








Input Form





Hypergeometric2F1[a, b, (a + b)/2 + 1, z] == (1/(z (b - a))) Gamma[(a + b)/2 + 1] (z^2 - z)^((2 - a - b)/4) (LegendreP[(a - b)/2, 1 - (a + b)/2, 3, 1 - 2 z] - LegendreP[(a - b)/2 - 1, 1 - (a + b)/2, 3, 1 - 2 z]) /; Re[z] <= 0








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_", ",", "b_", ",", RowBox[List[FractionBox[RowBox[List["a_", "+", "b_"]], "2"], "+", "1"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["a", "+", "b"]], "2"], "+", "1"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "z"]], ")"]], RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "-", "a", "-", "b"]], ")"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List[FractionBox[RowBox[List["a", "-", "b"]], "2"], ",", RowBox[List["1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], ",", "3", ",", RowBox[List["1", "-", RowBox[List["2", " ", "z"]]]]]], "]"]], "-", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List["a", "-", "b"]], "2"], "-", "1"]], ",", RowBox[List["1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], ",", "3", ",", RowBox[List["1", "-", RowBox[List["2", " ", "z"]]]]]], "]"]]]], ")"]]]], RowBox[List["z", " ", RowBox[List["(", RowBox[List["b", "-", "a"]], ")"]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]


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





2001-10-29