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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[11/4, 23/4, 11/2, z] == (1/(1463 Pi^(3/2) z^(9/2))) (8 (-((2 Sqrt[z] (-40 + 80 z - 27 z^2 - 13 z^3 + 32 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^3) - (2 Sqrt[z] (-40 + 80 z - 27 z^2 - 13 z^3 + 32 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^3 + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2)) ((80 - 120 Sqrt[z] - 100 z + 180 z^(3/2) - 15 z^2 - 12 z^(5/2) + 11 z^3 - 24 z^(7/2) + 32 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) ((80 + 120 Sqrt[z] - 100 z - 180 z^(3/2) - 15 z^2 + 12 z^(5/2) + 11 z^3 + 24 z^(7/2) + 32 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

 Standard Form

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 MathML Form

 2 F 1 ( 11 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["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[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 1463 π 3 / 2 z 9 / 2 ( 8 ( - 2 z ( 32 z 4 - 13 z 3 - 27 z 2 + 80 z - 40 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 3 - 2 z ( 32 z 4 - 13 z 3 - 27 z 2 + 80 z - 40 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 3 + ( 32 z 4 - 24 z 7 / 2 + 11 z 3 - 12 z 5 / 2 - 15 z 2 + 180 z 3 / 2 - 100 z - 120 z + 80 ) K ( 1 2 ( 1 - z ) ) ( z - 1 ) 3 ( z + 1 ) 2 + ( 32 z 4 + 24 z 7 / 2 + 11 z 3 + 12 z 5 / 2 - 15 z 2 - 180 z 3 / 2 - 100 z + 120 z + 80 ) K ( 1 2 ( z + 1 ) ) ( z - 1 ) 2 ( z + 1 ) 3 ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 11 4 23 4 11 2 z 1 1463 3 2 z 9 2 -1 8 -1 2 z 1 2 32 z 4 -1 13 z 3 -1 27 z 2 80 z -40 EllipticE 1 2 1 -1 z 1 2 z -1 3 -1 -1 2 z 1 2 32 z 4 -1 13 z 3 -1 27 z 2 80 z -40 EllipticE 1 2 z 1 2 1 z -1 3 -1 32 z 4 -1 24 z 7 2 11 z 3 -1 12 z 5 2 -1 15 z 2 180 z 3 2 -1 100 z -1 120 z 1 2 80 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 3 z 1 2 1 2 -1 32 z 4 24 z 7 2 11 z 3 12 z 5 2 -1 15 z 2 -1 180 z 3 2 -1 100 z 120 z 1 2 80 EllipticK 1 2 z 1 2 1 z 1 2 -1 2 z 1 2 1 3 -1 Gamma 1 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["11", "4"], ",", FractionBox["23", "4"], ",", FractionBox["11", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "40"]], "+", RowBox[List["80", " ", "z"]], "-", RowBox[List["27", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["13", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["32", " ", 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"]], ")"]], "3"]]]], "-", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "40"]], "+", RowBox[List["80", " ", "z"]], "-", RowBox[List["27", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["13", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["32", " ", 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"]], ")"]], "3"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["80", "-", RowBox[List["120", " ", SqrtBox["z"]]], "-", RowBox[List["100", " ", "z"]], "+", RowBox[List["180", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["12", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["32", " ", 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"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["80", "+", RowBox[List["120", " ", SqrtBox["z"]]], "-", RowBox[List["100", " ", "z"]], "-", RowBox[List["180", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["15", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["12", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["11", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["32", " ", 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"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["1463", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]

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

 2007-05-02