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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.an3q.01

 Input Form

 Hypergeometric2F1[17/4, 9/2, 5, z] == (256 Sqrt[2] (2 (1 - z)^(1/4) (-384 + 1408 z - 1888 z^2 + 1095 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-384 + 1408 z - 1888 z^2 + 1095 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-1 + z) (-384 + 1216 z - 1340 z^2 + 585 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-384 + 1408 z - 1888 z^2 + 1095 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-384 + 1408 z - 1888 z^2 + 1095 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-384 + 1408 z - 1888 z^2 + 1095 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (20475 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^4 z^4)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["17", "4"], ",", FractionBox["9", "2"], ",", "5", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["256", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "384"]], "+", RowBox[List["1408", " ", "z"]], "-", RowBox[List["1888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "384"]], "+", RowBox[List["1408", " ", "z"]], "-", RowBox[List["1888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "384"]], "+", RowBox[List["1216", " ", "z"]], "-", RowBox[List["1340", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["585", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "384"]], "+", RowBox[List["1408", " ", "z"]], "-", RowBox[List["1888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "384"]], "+", RowBox[List["1408", " ", "z"]], "-", RowBox[List["1888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "384"]], "+", RowBox[List["1408", " ", "z"]], "-", RowBox[List["1888", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", "z"]], RowBox[List["2", " ", "z"]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["20475", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "4"], " ", SuperscriptBox["z", "4"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 17 4 , 9 2 ; 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["17", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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] ( 256 2 ( 2 ( 1 - z ) 3 / 4 ( 1095 z 3 - 1888 z 2 + 1408 z - 384 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 2 1 - z 4 ( 1095 z 3 - 1888 z 2 + 1408 z - 384 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( z - 1 ) ( 585 z 3 - 1340 z 2 + 1216 z - 384 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 1 - z ) 3 / 4 ( 1095 z 3 - 1888 z 2 + 1408 z - 384 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z ( 1095 z 3 - 1888 z 2 + 1408 z - 384 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z 4 ( 1095 z 3 - 1888 z 2 + 1408 z - 384 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 20475 π 1 - z + 1 ( z - 1 ) 4 z 4 ) HypergeometricPFQ 17 4 9 2 5 z 256 2 1 2 2 1 -1 z 3 4 1095 z 3 -1 1888 z 2 1408 z -384 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 2 1 -1 z 1 4 1095 z 3 -1 1888 z 2 1408 z -384 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 z -1 585 z 3 -1 1340 z 2 1216 z -384 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 3 4 1095 z 3 -1 1888 z 2 1408 z -384 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 2 1095 z 3 -1 1888 z 2 1408 z -384 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 4 1095 z 3 -1 1888 z 2 1408 z -384 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 20475 1 -1 z 1 2 1 1 2 z -1 4 z 4 -1 [/itex]

 Rule Form

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

 2007-05-02