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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.an2p.01









  


  








Input Form





Hypergeometric2F1[17/4, 17/4, 7/2, z] == (1/(7605 Pi^(3/2) z^(5/2))) (8 ((2 (36 - 249 z + 1254 z^2 + 1007 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^5 - (2 (36 - 249 z + 1254 z^2 + 1007 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^5 - ((36 - 18 Sqrt[z] - 231 z + 108 z^(3/2) + 1146 z^2 + 422 z^(5/2) + 585 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4) - ((36 + 18 Sqrt[z] - 231 z - 108 z^(3/2) + 1146 z^2 - 422 z^(5/2) + 585 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/ ((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) Gamma[3/4]^2)








Standard Form





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MathML Form







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</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["7", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["36", "-", RowBox[List["249", " ", "z"]], "+", RowBox[List["1254", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1007", " ", 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"]], ")"]], "5"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["36", "-", RowBox[List["249", " ", "z"]], "+", RowBox[List["1254", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1007", " ", 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"]], ")"]], "5"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["36", "-", RowBox[List["18", " ", SqrtBox["z"]]], "-", RowBox[List["231", " ", "z"]], "+", RowBox[List["108", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["1146", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["422", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["585", " ", 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"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["36", "+", RowBox[List["18", " ", SqrtBox["z"]]], "-", RowBox[List["231", " ", "z"]], "-", RowBox[List["108", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["1146", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["422", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["585", " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["7605", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]


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





2007-05-02