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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/07.23.03.0096.01









  


  








Input Form





Hypergeometric2F1[a, b, a - b + 2, z] == ((Gamma[a - b + 2]/(b - 1)) (-z)^((b - a - 1)/2) (a LegendreP[-b, b - a - 1, 2, (1 + z)/(1 - z)] - Sqrt[-z] LegendreP[-b, b - a, 2, (1 + z)/(1 - z)]))/(1 - z)^b /; !IntervalMemberQ[Interval[{1, Infinity}], z]








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["a_", "-", "b_", "+", "2"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", "-", "b", "+", "2"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["b", "-", "a", "-", "1"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["-", "b"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["-", "b"]], ",", RowBox[List["b", "-", "a", "-", "1"]], ",", "2", ",", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["1", "-", "z"]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["-", "z"]]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List["-", "b"]], ",", RowBox[List["b", "-", "a"]], ",", "2", ",", FractionBox[RowBox[List["1", "+", "z"]], RowBox[List["1", "-", "z"]]]]], "]"]]]]]], ")"]]]], RowBox[List["b", "-", "1"]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29