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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=-31/8, b>=a > For fixed z and a=-31/8, b=11/8





http://functions.wolfram.com/07.23.03.bf68.01









  


  










Input Form





Hypergeometric2F1[-(31/8), 11/8, 2, z] == (16 2^(1/4) (-2 Sqrt[1 - z] (24955 - 166498 z + 285051 z^2 - 203268 z^3 + 53040 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (24955 - 166498 z + 285051 z^2 - 203268 z^3 + 53040 z^4) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (24955 - 166498 z + 285051 z^2 - 203268 z^3 + 53040 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (24955 + 182872 z - 602849 z^2 + 780702 z^3 - 464880 z^4 + 106080 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (2919735 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z)










Standard Form





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MathML Form







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</apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </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["31", "8"]]], ",", FractionBox["11", "8"], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["24955", "-", RowBox[List["166498", " ", "z"]], "+", RowBox[List["285051", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["203268", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["53040", " ", 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["24955", "-", RowBox[List["166498", " ", "z"]], "+", RowBox[List["285051", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["203268", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["53040", " ", 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["24955", "-", RowBox[List["166498", " ", "z"]], "+", RowBox[List["285051", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["203268", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["53040", " ", 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[RowBox[List["(", RowBox[List["24955", "+", RowBox[List["182872", " ", "z"]], "-", RowBox[List["602849", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["780702", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["464880", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["106080", " ", 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["2919735", " ", "\[Pi]", " ", SqrtBox[RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]], " ", "z"]]]]]]]










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





2007-05-02