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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=35/8





http://functions.wolfram.com/07.23.03.c8w8.01









  


  










Input Form





Hypergeometric2F1[23/8, 35/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-128 + 363 z - 315 z^2 + 140 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (128 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 3 (137 + 121 Sqrt[1 - z] + 121 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + (438 + 315 Sqrt[1 - z] + 315 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 35 (1 + 4 Sqrt[1 - z] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (197505 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(13/4) z^3)










Standard Form





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MathML Form







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</apply> </apply> <cn type='rational'> 13 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </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[FractionBox["23", "8"], ",", FractionBox["35", "8"], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2048", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "128"]], "+", RowBox[List["363", " ", "z"]], "-", RowBox[List["315", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["140", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["128", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List["137", "+", RowBox[List["121", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["121", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["438", "+", RowBox[List["315", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["315", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["35", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["197505", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["13", "/", "4"]]], " ", SuperscriptBox["z", "3"]]]]]]]]










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





2007-05-02