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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[11/4, 11/4, -(1/2), z] == (1/(1176 Pi^(3/2))) ((-((4 (-147 + 3087 z + 13723 z^2 + 3817 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^6) - (4 (-147 + 3087 z + 13723 z^2 + 3817 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/ (-1 + z)^6 + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((-294 + 147 Sqrt[z] + 6027 z + 6554 z^(3/2) + 20892 z^2 + 3539 z^(5/2) + 4095 z^3) EllipticK[(1/2) (1 - Sqrt[z])]) + ((294 + 147 Sqrt[z] - 6027 z + 6554 z^(3/2) - 20892 z^2 + 3539 z^(5/2) - 4095 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) Gamma[1/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["11", "4"], ",", FractionBox["11", "4"], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1176", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "147"]], "+", RowBox[List["3087", " ", "z"]], "+", RowBox[List["13723", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3817", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "147"]], "+", RowBox[List["3087", " ", "z"]], "+", RowBox[List["13723", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3817", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "294"]], "+", RowBox[List["147", " ", SqrtBox["z"]]], "+", RowBox[List["6027", " ", "z"]], "+", RowBox[List["6554", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["20892", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3539", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["294", "+", RowBox[List["147", " ", SqrtBox["z"]]], "-", RowBox[List["6027", " ", "z"]], "+", RowBox[List["6554", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["20892", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3539", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["4095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 11 4 , 11 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["11", "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 1176 π 3 / 2 ( ( - 4 ( 3817 z 3 + 13723 z 2 + 3087 z - 147 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 6 - 4 ( 3817 z 3 + 13723 z 2 + 3087 z - 147 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 6 + ( 4095 z 3 + 3539 z 5 / 2 + 20892 z 2 + 6554 z 3 / 2 + 6027 z + 147 z - 294 ) K ( 1 2 ( 1 - z ) ) ( z - 1 ) 6 ( z + 1 ) 5 + ( - 4095 z 3 + 3539 z 5 / 2 - 20892 z 2 + 6554 z 3 / 2 - 6027 z + 147 z + 294 ) K ( 1 2 ( z + 1 ) ) ( z - 1 ) 5 ( z + 1 ) 6 ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 11 4 11 4 -1 1 2 z 1 1176 3 2 -1 -1 4 3817 z 3 13723 z 2 3087 z -147 EllipticE 1 2 1 -1 z 1 2 z -1 6 -1 -1 4 3817 z 3 13723 z 2 3087 z -147 EllipticE 1 2 z 1 2 1 z -1 6 -1 4095 z 3 3539 z 5 2 20892 z 2 6554 z 3 2 6027 z 147 z 1 2 -294 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 6 z 1 2 1 5 -1 -4095 z 3 3539 z 5 2 -1 20892 z 2 6554 z 3 2 -1 6027 z 147 z 1 2 294 EllipticK 1 2 z 1 2 1 z 1 2 -1 5 z 1 2 1 6 -1 Gamma 1 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["11", "4"], ",", FractionBox["11", "4"], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "147"]], "+", RowBox[List["3087", " ", "z"]], "+", RowBox[List["13723", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3817", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "147"]], "+", RowBox[List["3087", " ", "z"]], "+", RowBox[List["13723", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3817", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "294"]], "+", RowBox[List["147", " ", SqrtBox["z"]]], "+", RowBox[List["6027", " ", "z"]], "+", RowBox[List["6554", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["20892", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3539", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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"]]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["294", "+", RowBox[List["147", " ", SqrtBox["z"]]], "-", RowBox[List["6027", " ", "z"]], "+", RowBox[List["6554", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["20892", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3539", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["4095", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", 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"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["1176", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02