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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=-1/8, b>=a > For fixed z and a=-1/8, b=29/8





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









  


  








Input Form





Hypergeometric2F1[-(1/8), 29/8, 1, z] == (1/(1365 Pi (-1 + z)^3)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (16 (-1 + z) (452 - 917 z + 462 z^2) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (273 - 593 z + 308 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])/z - 8 (-1 + z) (452 - 917 z + 462 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-455 + 1591 z - 1736 z^2 + 616 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))








Standard Form





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MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], ",", FractionBox["29", "8"], ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["452", "-", RowBox[List["917", " ", "z"]], "+", RowBox[List["462", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", FractionBox[RowBox[List["5", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["273", "-", RowBox[List["593", " ", "z"]], "+", RowBox[List["308", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "z"], "-", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["452", "-", RowBox[List["917", " ", "z"]], "+", RowBox[List["462", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", FractionBox[RowBox[List["3", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "455"]], "+", RowBox[List["1591", " ", "z"]], "-", RowBox[List["1736", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["616", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "z"]]], ")"]]]], RowBox[List["1365", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"]]]]]]]]


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





2007-05-02