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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 > Generalized cases involving algebraic functions with squares in arguments





http://functions.wolfram.com/07.23.26.0222.01









  


  










Input Form





(-z + Sqrt[1 + z^2])^a Hypergeometric2F1[a, b, 1 + a, (1 + 2 z^2 - 2 z Sqrt[1 + z^2])/(2 z^2 - 2 z Sqrt[1 + z^2])] == (1/Sqrt[Pi]) 2^(-1 + b) a MeijerG[{{1 - a/2}, {(2 + a)/2, a/2 + b}}, {{b/2, (1 + b)/2, a/2}, {}}, z, 1/2] /; Re[z] > 0










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










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





2001-10-29





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