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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.alz7.01

 Input Form

 Hypergeometric2F1[11/4, 23/4, -(1/2), z] == (1/(35112 Pi^(3/2))) (((1/(-1 + z)^9) (2 (-8778 + 355509 z + 3852400 z^2 + 4027510 z^3 + 179010 z^4 - 18291 z^5 + 1248 z^6) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^9) (2 (-8778 + 355509 z + 3852400 z^2 + 4027510 z^3 + 179010 z^4 - 18291 z^5 + 1248 z^6) EllipticE[(1/2) (1 + Sqrt[z])]) - (1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8)) ((-8778 + 4389 Sqrt[z] + 351120 z + 634300 z^(3/2) + 3218100 z^2 + 1308430 z^(5/2) + 2719080 z^3 + 166140 z^(7/2) + 12870 z^4 - 17355 z^(9/2) - 936 z^5 + 1248 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9)) ((8778 + 4389 Sqrt[z] - 351120 z + 634300 z^(3/2) - 3218100 z^2 + 1308430 z^(5/2) - 2719080 z^3 + 166140 z^(7/2) - 12870 z^4 - 17355 z^(9/2) + 936 z^5 + 1248 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["11", "4"], ",", FractionBox["23", "4"], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["35112", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8778"]], "+", RowBox[List["355509", " ", "z"]], "+", RowBox[List["3852400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4027510", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["179010", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["18291", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1248", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "9"]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8778"]], "+", RowBox[List["355509", " ", "z"]], "+", RowBox[List["3852400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4027510", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["179010", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["18291", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1248", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "9"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "8"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "8778"]], "+", RowBox[List["4389", " ", SqrtBox["z"]]], "+", RowBox[List["351120", " ", "z"]], "+", RowBox[List["634300", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["3218100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1308430", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["2719080", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["166140", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["12870", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["17355", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["936", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1248", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "8"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "9"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["8778", "+", RowBox[List["4389", " ", SqrtBox["z"]]], "-", RowBox[List["351120", " ", "z"]], "+", RowBox[List["634300", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["3218100", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1308430", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["2719080", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["166140", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["12870", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["17355", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["936", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1248", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]]]], ")"]], " ", 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 ( 11 4 , 23 4 ; - 1 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["11", "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[RowBox[List["-", FractionBox["1", "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 35112 π 3 / 2 ( ( 1 ( z - 1 ) 9 2 ( 1248 z 6 - 18291 z 5 + 179010 z 4 + 4027510 z 3 + 3852400 z 2 + 355509 z - 8778 ) E ( 1 2 ( 1 - z ) ) + 1 ( z - 1 ) 9 2 ( 1248 z 6 - 18291 z 5 + 179010 z 4 + 4027510 z 3 + 3852400 z 2 + 355509 z - 8778 ) E ( 1 2 ( z + 1 ) ) - 1 ( z - 1 ) 9 ( z + 1 ) 8 ( ( 1248 z 11 / 2 - 936 z 5 - 17355 z 9 / 2 + 12870 z 4 + 166140 z 7 / 2 + 2719080 z 3 + 1308430 z 5 / 2 + 3218100 z 2 + 634300 z 3 / 2 + 351120 z + 4389 z - 8778 ) K ( 1 2 ( 1 - z ) ) ) - 1 ( z - 1 ) 8 ( z + 1 ) 9 ( ( 1248 z 11 / 2 + 936 z 5 - 17355 z 9 / 2 - 12870 z 4 + 166140 z 7 / 2 - 2719080 z 3 + 1308430 z 5 / 2 - 3218100 z 2 + 634300 z 3 / 2 - 351120 z + 4389 z + 8778 ) K ( 1 2 ( z + 1 ) ) ) ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 11 4 23 4 -1 1 2 z 1 35112 3 2 -1 1 z -1 9 -1 2 1248 z 6 -1 18291 z 5 179010 z 4 4027510 z 3 3852400 z 2 355509 z -8778 EllipticE 1 2 1 -1 z 1 2 1 z -1 9 -1 2 1248 z 6 -1 18291 z 5 179010 z 4 4027510 z 3 3852400 z 2 355509 z -8778 EllipticE 1 2 z 1 2 1 -1 1 z 1 2 -1 9 z 1 2 1 8 -1 1248 z 11 2 -1 936 z 5 -1 17355 z 9 2 12870 z 4 166140 z 7 2 2719080 z 3 1308430 z 5 2 3218100 z 2 634300 z 3 2 351120 z 4389 z 1 2 -8778 EllipticK 1 2 1 -1 z 1 2 -1 1 z 1 2 -1 8 z 1 2 1 9 -1 1248 z 11 2 936 z 5 -1 17355 z 9 2 -1 12870 z 4 166140 z 7 2 -1 2719080 z 3 1308430 z 5 2 -1 3218100 z 2 634300 z 3 2 -1 351120 z 4389 z 1 2 8778 EllipticK 1 2 z 1 2 1 Gamma 1 4 2 [/itex]

 Rule Form

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

 2007-05-02