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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[7/4, 23/4, 11/2, z] == (1/(16093 Pi^(3/2) z^(9/2))) (8 ((8 Sqrt[z] (70 - 45 z - 24 z^2 - 20 z^3 + 96 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^2 + (8 Sqrt[z] (70 - 45 z - 24 z^2 - 20 z^3 + 96 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^2 - (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z]))) ((-560 + 840 Sqrt[z] - 60 z - 120 z^(3/2) + 105 z^2 - 201 z^(5/2) + 208 z^3 - 288 z^(7/2) + 384 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/(-1 - Sqrt[z] + z + z^(3/2))) ((-560 - 840 Sqrt[z] - 60 z + 120 z^(3/2) + 105 z^2 + 201 z^(5/2) + 208 z^3 + 288 z^(7/2) + 384 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "4"], ",", FractionBox["23", "4"], ",", FractionBox["11", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["16093", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List["8", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["45", " ", "z"]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["20", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["45", " ", "z"]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["20", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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"]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "560"]], "+", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["60", " ", "z"]], "-", RowBox[List["120", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["105", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["201", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["288", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "-", SqrtBox["z"], "+", "z", "+", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "560"]], "-", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["60", " ", "z"]], "+", RowBox[List["120", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["105", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["201", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["288", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 7 4 , 23 4 ; 11 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["23", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["11", "2"], 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 16093 π 3 / 2 z 9 / 2 ( 8 ( 8 z ( 96 z 4 - 20 z 3 - 24 z 2 - 45 z + 70 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 2 + 8 z ( 96 z 4 - 20 z 3 - 24 z 2 - 45 z + 70 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 2 - 1 ( z - 1 ) 2 ( z + 1 ) ( 384 z 4 - 288 z 7 / 2 + 208 z 3 - 201 z 5 / 2 + 105 z 2 - 120 z 3 / 2 - 60 z + 840 z - 560 ) K ( 1 2 ( 1 - z ) ) - 1 z 3 / 2 + z - z - 1 ( 384 z 4 + 288 z 7 / 2 + 208 z 3 + 201 z 5 / 2 + 105 z 2 + 120 z 3 / 2 - 60 z - 840 z - 560 ) K ( 1 2 ( z + 1 ) ) ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 7 4 23 4 11 2 z 1 16093 3 2 z 9 2 -1 8 8 z 1 2 96 z 4 -1 20 z 3 -1 24 z 2 -1 45 z 70 EllipticE 1 2 1 -1 z 1 2 z -1 2 -1 8 z 1 2 96 z 4 -1 20 z 3 -1 24 z 2 -1 45 z 70 EllipticE 1 2 z 1 2 1 z -1 2 -1 -1 1 z 1 2 -1 2 z 1 2 1 -1 384 z 4 -1 288 z 7 2 208 z 3 -1 201 z 5 2 105 z 2 -1 120 z 3 2 -1 60 z 840 z 1 2 -560 EllipticK 1 2 1 -1 z 1 2 -1 1 z 3 2 z -1 z 1 2 -1 -1 384 z 4 288 z 7 2 208 z 3 201 z 5 2 105 z 2 120 z 3 2 -1 60 z -1 840 z 1 2 -560 EllipticK 1 2 z 1 2 1 Gamma 1 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "4"], ",", FractionBox["23", "4"], ",", FractionBox["11", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["45", " ", "z"]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["20", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["45", " ", "z"]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["20", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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[RowBox[List["-", "560"]], "+", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["60", " ", "z"]], "-", RowBox[List["120", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["105", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["201", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["288", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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[RowBox[List["-", "560"]], "-", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["60", " ", "z"]], "+", RowBox[List["120", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["105", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["201", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["288", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["1", "4"], "]"]], "2"]]], RowBox[List["16093", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]

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

 2007-05-02