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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=-7/4, b>=a > For fixed z and a=-7/4, b=-3/4





http://functions.wolfram.com/07.23.03.aet9.01









  


  










Input Form





Hypergeometric2F1[-(7/4), -(3/4), -(9/2), z] == (1/(480 Pi^(3/2))) ((-((2 Sqrt[z] (-240 + 460 z - 227 z^2 + 11 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^2) + (2 Sqrt[z] (-240 + 460 z - 227 z^2 + 11 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^2 + ((480 - 720 Sqrt[z] - 560 z + 1020 z^(3/2) + 70 z^2 - 297 z^(5/2) + 11 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^2 (1 + Sqrt[z])) - (1/(-1 - Sqrt[z] + z + z^(3/2))) ((480 + 720 Sqrt[z] - 560 z - 1020 z^(3/2) + 70 z^2 + 297 z^(5/2) + 11 z^3) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)










Standard Form





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MathML Form







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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[RowBox[List["-", FractionBox["7", "4"]]], ",", RowBox[List["-", FractionBox["3", "4"]]], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "240"]], "+", RowBox[List["460", " ", "z"]], "-", RowBox[List["227", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["11", " ", 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"]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "240"]], "+", RowBox[List["460", " ", "z"]], "-", RowBox[List["227", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["11", " ", 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"]], ")"]], "2"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["480", "-", RowBox[List["720", " ", SqrtBox["z"]]], "-", RowBox[List["560", " ", "z"]], "+", RowBox[List["1020", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["70", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["297", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11", " ", 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"]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["480", "+", RowBox[List["720", " ", SqrtBox["z"]]], "-", RowBox[List["560", " ", "z"]], "-", RowBox[List["1020", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["70", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["297", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "-", SqrtBox["z"], "+", "z", "+", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["480", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]










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





2007-05-02