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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/07.23.26.0045.01









  


  










Input Form





Hypergeometric2F1[a, b, 1 + b, (-Sqrt[z] + Sqrt[1 + z])/ (Sqrt[z] + Sqrt[1 + z])]/(Sqrt[z] + Sqrt[1 + z])^(2 b) == (b/(2^a Sqrt[Pi])) MeijerG[{{1 - b}, {1, 1 - a + b}}, {{0, (1 - a)/2, 1 - a/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[SqrtBox["z_"], "+", SqrtBox[RowBox[List["1", "+", "z_"]]]]], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", "b_"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", RowBox[List["1", "+", "b_"]], ",", FractionBox[RowBox[List[RowBox[List["-", SqrtBox["z_"]]], "+", SqrtBox[RowBox[List["1", "+", "z_"]]]]], RowBox[List[SqrtBox["z_"], "+", SqrtBox[RowBox[List["1", "+", "z_"]]]]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "a"]]], " ", "b"]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", "b"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "-", "a", "+", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox[RowBox[List["1", "-", "a"]], "2"], ",", RowBox[List["1", "-", FractionBox["a", "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





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