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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions with squares in arguments





http://functions.wolfram.com/07.23.26.0049.01









  


  










Input Form





(-Sqrt[z] + Sqrt[1 + z])^(-2 - b + 2 c) Hypergeometric2F1[1, b, c, (1 + 2 z - 2 Sqrt[z] Sqrt[1 + z])/(2 z - 2 Sqrt[z] Sqrt[1 + z])] == ((c - 1)/Sqrt[Pi]) MeijerG[{{2 + b/2 - c}, {1 + b/2, -(b/2) + c}}, {{1/2, 1, b/2}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", SqrtBox["z_"]]], "+", SqrtBox[RowBox[List["1", "+", "z_"]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "-", "b_", "+", RowBox[List["2", " ", "c_"]]]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "b_", ",", "c_", ",", FractionBox[RowBox[List["1", "+", RowBox[List["2", " ", "z_"]], "-", RowBox[List["2", " ", SqrtBox["z_"], " ", SqrtBox[RowBox[List["1", "+", "z_"]]]]]]], RowBox[List[RowBox[List["2", " ", "z_"]], "-", RowBox[List["2", " ", SqrtBox["z_"], " ", SqrtBox[RowBox[List["1", "+", "z_"]]]]]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["c", "-", "1"]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", "+", FractionBox["b", "2"], "-", "c"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", FractionBox["b", "2"]]], ",", RowBox[List[RowBox[List["-", FractionBox["b", "2"]]], "+", "c"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", FractionBox["b", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], SqrtBox["\[Pi]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29