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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/07.24.03.0087.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, a + b + 3/2, z] == ((1/(2 a + 1)) (Sqrt[-z] LegendreP[b - a - 1/2, 1/2 - a - b, 3, Sqrt[1 - z]] - 2 b LegendreP[b - a + 1/2, -(1/2) - a - b, 3, Sqrt[1 - z]]))/(-(z/4))^((1 + 2 a + 2 b)/4) /; !IntervalMemberQ[Interval[{0, 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["3", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["z", "4"]]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["-", "z"]]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["b", "-", "a", "-", FractionBox["1", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "-", "a", "-", "b"]], ",", "3", ",", SqrtBox[RowBox[List["1", "-", "z"]]]]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["b", "-", "a", "+", FractionBox["1", "2"]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "a", "-", "b"]], ",", "3", ",", SqrtBox[RowBox[List["1", "-", "z"]]]]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", "1"]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29