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





http://functions.wolfram.com/07.23.03.an2h.01









  


  








Input Form





Hypergeometric2F1[17/4, 17/4, 3/2, z] == (1/(114075 Pi^(3/2) Sqrt[z])) (2 ((2 (17787 + 349455 z + 527729 z^2 + 88069 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7 - (2 (17787 + 349455 z + 527729 z^2 + 88069 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 - (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((17787 + 48144 Sqrt[z] + 301311 z + 154592 z^(3/2) + 373137 z^2 + 43024 z^(5/2) + 45045 z^3) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((17787 - 48144 Sqrt[z] + 301311 z - 154592 z^(3/2) + 373137 z^2 - 43024 z^(5/2) + 45045 z^3) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)








Standard Form





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MathML Form







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z </ci> </apply> <cn type='integer'> 17787 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 88069 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 527729 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 349455 </cn> <ci> z </ci> </apply> <cn type='integer'> 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</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["17", "4"], ",", FractionBox["17", "4"], ",", FractionBox["3", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17787", "+", RowBox[List["349455", " ", "z"]], "+", RowBox[List["527729", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["88069", " ", 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"]], ")"]], "7"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17787", "+", RowBox[List["349455", " ", "z"]], "+", RowBox[List["527729", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["88069", " ", 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"]], ")"]], "7"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["17787", "+", RowBox[List["48144", " ", SqrtBox["z"]]], "+", RowBox[List["301311", " ", "z"]], "+", RowBox[List["154592", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["373137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["43024", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["45045", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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"]]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["17787", "-", RowBox[List["48144", " ", SqrtBox["z"]]], "+", RowBox[List["301311", " ", "z"]], "-", RowBox[List["154592", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["373137", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["43024", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["45045", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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"]]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "7"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["114075", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SqrtBox["z"]]]]]]]]


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





2007-05-02