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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions and 2F1with algebraic arguments





http://functions.wolfram.com/07.24.26.0181.01









  


  








Input Form





(Hypergeometric2F1Regularized[a, b, 1 + a - b, (-Sqrt[z] + Sqrt[1 + z])/ (Sqrt[z] + Sqrt[1 + z])] Hypergeometric2F1[a, b, 1 + a - b, (-Sqrt[z] + Sqrt[1 + z])/(Sqrt[z] + Sqrt[1 + z])])/ (Sqrt[z] + Sqrt[1 + z])^(2 a) == (Gamma[1 + a - b]/(4^b (Sqrt[Pi] Gamma[a] Gamma[1 + a - 2 b]))) MeijerG[{{1 - a}, {1 - b, 1 + a - 2 b}}, {{0, 1 - 2 b, 1/2 - b}, {}}, 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"]], " ", "a_"]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a_", ",", "b_", ",", RowBox[List["1", "+", "a_", "-", "b_"]], ",", FractionBox[RowBox[List[RowBox[List["-", SqrtBox["z_"]]], "+", SqrtBox[RowBox[List["1", "+", "z_"]]]]], RowBox[List[SqrtBox["z_"], "+", SqrtBox[RowBox[List["1", "+", "z_"]]]]]]]], "]"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", RowBox[List["1", "+", "a_", "-", "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["4", RowBox[List["-", "b"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "a", "-", "b"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", "a"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "b"]], ",", RowBox[List["1", "+", "a", "-", RowBox[List["2", " ", "b"]]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", RowBox[List["2", " ", "b"]]]], ",", RowBox[List[FractionBox["1", "2"], "-", "b"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "a", "-", RowBox[List["2", " ", "b"]]]], "]"]]]]], "/;", 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