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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 8 and fixed z and a<0 > For fixed z and a=-23/8, b>=a > For fixed z and a=-23/8, b=-13/8





http://functions.wolfram.com/07.23.03.bjqg.01









  


  










Input Form





Hypergeometric2F1[-(23/8), -(13/8), 3, z] == (256 2^(1/4) (2 Sqrt[1 - z] (-920 + 15755 z + 235023 z^2 + 153761 z^3 + 1885 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-920 + 15755 z + 235023 z^2 + 153761 z^3 + 1885 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-920 + 15755 z + 235023 z^2 + 153761 z^3 + 1885 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 (-460 + 8165 z - 218116 z^2 - 496922 z^3 - 105560 z^4 + 1885 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (84672315 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^2)










Standard Form





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MathML Form







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</apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "8"]]], ",", RowBox[List["-", FractionBox["13", "8"]]], ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "920"]], "+", RowBox[List["15755", " ", "z"]], "+", RowBox[List["235023", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["153761", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1885", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["2", "-", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "920"]], "+", RowBox[List["15755", " ", "z"]], "+", RowBox[List["235023", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["153761", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1885", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "920"]], "+", RowBox[List["15755", " ", "z"]], "+", RowBox[List["235023", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["153761", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1885", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "460"]], "+", RowBox[List["8165", " ", "z"]], "-", RowBox[List["218116", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["496922", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["105560", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1885", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["84672315", " ", "\[Pi]", " ", SqrtBox[RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]], " ", SuperscriptBox["z", "2"]]]]]]]]










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





2007-05-02