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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Identities > Functional identities > Generic general cases





http://functions.wolfram.com/07.23.17.0056.01









  


  








Input Form





Hypergeometric2F1[a, b, c, z] == Hypergeometric2F1[c - a, b, c, z/(z - 1)]/ (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_", ",", "c_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["-", "b"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["c", "-", "a"]], ",", "b", ",", "c", ",", FractionBox["z", RowBox[List["z", "-", "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