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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 4 and fixed z > For fixed z and a=5/4, b>=a > For fixed z and a=5/4, b=17/4





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









  


  








Input Form





Hypergeometric2F1[5/4, 17/4, 3/2, z] == (1/(585 Pi^(3/2) Sqrt[z])) (2 (-((2 (231 + 258 z - 137 z^2 + 32 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^4) + (2 (231 + 258 z - 137 z^2 + 32 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^4 + ((231 + 177 Sqrt[z] + 81 z - 113 z^(3/2) - 24 z^2 + 32 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3) - ((-231 + 177 Sqrt[z] - 81 z - 113 z^(3/2) + 24 z^2 + 32 z^(5/2)) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) Gamma[3/4]^2)








Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["17", "4"], ",", FractionBox["3", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["231", "+", RowBox[List["258", " ", "z"]], "-", RowBox[List["137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["231", "+", RowBox[List["258", " ", "z"]], "-", RowBox[List["137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["231", "+", RowBox[List["177", " ", SqrtBox["z"]]], "+", RowBox[List["81", " ", "z"]], "-", RowBox[List["113", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "231"]], "+", RowBox[List["177", " ", SqrtBox["z"]]], "-", RowBox[List["81", " ", "z"]], "-", RowBox[List["113", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["585", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SqrtBox["z"]]]]]]]]


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





2007-05-02