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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aee1.01

 Input Form

 Hypergeometric2F1[-(9/4), 9/4, 6, z] == (1/(777251475 Pi Sqrt[1 + Sqrt[z]] z^5)) (16384 ((18432 + 18432 Sqrt[z] - 88416 z - 88416 z^(3/2) + 152139 z^2 + 152139 z^(5/2) - 86625 z^3 - 86625 z^(7/2) - 38115 z^4 - 38115 z^(9/2) + 175021 z^5 + 175021 z^(11/2) - 117348 z^6 - 117348 z^(13/2) + 25872 z^7 + 25872 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (18432 - 93024 z + 172947 z^2 - 119145 z^3 - 24255 z^4 + 91861 z^5 - 59752 z^6 + 12936 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "4"]]], ",", FractionBox["9", "4"], ",", "6", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["777251475", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox["z"]]]], " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["16384", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["18432", "+", RowBox[List["18432", " ", SqrtBox["z"]]], "-", RowBox[List["88416", " ", "z"]], "-", RowBox[List["88416", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["152139", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["152139", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["86625", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["86625", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["38115", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["38115", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["175021", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["175021", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["117348", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["117348", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "+", RowBox[List["25872", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["25872", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["18432", "-", RowBox[List["93024", " ", "z"]], "+", RowBox[List["172947", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["119145", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["24255", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["91861", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["59752", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["12936", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 9 4 , 9 4 ; 6 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["9", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 777251475 π z + 1 z 5 ( 16384 ( ( 25872 z 15 / 2 + 25872 z 7 - 117348 z 13 / 2 - 117348 z 6 + 175021 z 11 / 2 + 175021 z 5 - 38115 z 9 / 2 - 38115 z 4 - 86625 z 7 / 2 - 86625 z 3 + 152139 z 5 / 2 + 152139 z 2 - 88416 z 3 / 2 - 88416 z + 18432 z + 18432 ) E ( 2 z z + 1 ) - ( 12936 z 7 - 59752 z 6 + 91861 z 5 - 24255 z 4 - 119145 z 3 + 172947 z 2 - 93024 z + 18432 ) K ( 2 z z + 1 ) ) ) HypergeometricPFQ -1 9 4 9 4 6 z 1 777251475 z 1 2 1 1 2 z 5 -1 16384 25872 z 15 2 25872 z 7 -1 117348 z 13 2 -1 117348 z 6 175021 z 11 2 175021 z 5 -1 38115 z 9 2 -1 38115 z 4 -1 86625 z 7 2 -1 86625 z 3 152139 z 5 2 152139 z 2 -1 88416 z 3 2 -1 88416 z 18432 z 1 2 18432 EllipticE 2 z 1 2 z 1 2 1 -1 -1 12936 z 7 -1 59752 z 6 91861 z 5 -1 24255 z 4 -1 119145 z 3 172947 z 2 -1 93024 z 18432 EllipticK 2 z 1 2 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02