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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/4, 17/4, 1/2, z] == (1/(195 Pi^(3/2))) (((32 Sqrt[z] (-30 + 45 z - 31 z^2 + 8 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^4 - (32 Sqrt[z] (-30 + 45 z - 31 z^2 + 8 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^4 + ((195 + 285 Sqrt[z] - 435 z - 285 z^(3/2) + 400 z^2 + 96 z^(5/2) - 128 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3) + ((-195 + 285 Sqrt[z] + 435 z - 285 z^(3/2) - 400 z^2 + 96 z^(5/2) + 128 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/ ((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "4"], ",", FractionBox["17", "4"], ",", FractionBox["1", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["195", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["32", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "30"]], "+", RowBox[List["45", " ", "z"]], "-", RowBox[List["31", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", 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"]], ")"]], "4"]], "-", FractionBox[RowBox[List["32", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "30"]], "+", RowBox[List["45", " ", "z"]], "-", RowBox[List["31", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", 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"]], ")"]], "4"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["195", "+", RowBox[List["285", " ", SqrtBox["z"]]], "-", RowBox[List["435", " ", "z"]], "-", RowBox[List["285", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["128", " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "195"]], "+", RowBox[List["285", " ", SqrtBox["z"]]], "+", RowBox[List["435", " ", "z"]], "-", RowBox[List["285", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["128", " ", 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"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 1 4 , 17 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["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[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] 1 195 π 3 / 2 ( ( 32 z ( 8 z 3 - 31 z 2 + 45 z - 30 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 4 - 32 z ( 8 z 3 - 31 z 2 + 45 z - 30 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 4 + ( - 128 z 3 + 96 z 5 / 2 + 400 z 2 - 285 z 3 / 2 - 435 z + 285 z + 195 ) K ( 1 2 ( 1 - z ) ) ( z - 1 ) 4 ( z + 1 ) 3 + ( 128 z 3 + 96 z 5 / 2 - 400 z 2 - 285 z 3 / 2 + 435 z + 285 z - 195 ) K ( 1 2 ( z + 1 ) ) ( z - 1 ) 3 ( z + 1 ) 4 ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 1 4 17 4 1 2 z 1 195 3 2 -1 32 z 1 2 8 z 3 -1 31 z 2 45 z -30 EllipticE 1 2 1 -1 z 1 2 z -1 4 -1 -1 32 z 1 2 8 z 3 -1 31 z 2 45 z -30 EllipticE 1 2 z 1 2 1 z -1 4 -1 -128 z 3 96 z 5 2 400 z 2 -1 285 z 3 2 -1 435 z 285 z 1 2 195 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 4 z 1 2 1 3 -1 128 z 3 96 z 5 2 -1 400 z 2 -1 285 z 3 2 435 z 285 z 1 2 -195 EllipticK 1 2 z 1 2 1 z 1 2 -1 3 z 1 2 1 4 -1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "4"], ",", FractionBox["17", "4"], ",", FractionBox["1", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["32", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "30"]], "+", RowBox[List["45", " ", "z"]], "-", RowBox[List["31", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", 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"]], ")"]], "4"]], "-", FractionBox[RowBox[List["32", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "30"]], "+", RowBox[List["45", " ", "z"]], "-", RowBox[List["31", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", 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"]], ")"]], "4"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["195", "+", RowBox[List["285", " ", SqrtBox["z"]]], "-", RowBox[List["435", " ", "z"]], "-", RowBox[List["285", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["128", " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "195"]], "+", RowBox[List["285", " ", SqrtBox["z"]]], "+", RowBox[List["435", " ", "z"]], "-", RowBox[List["285", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["400", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["96", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["128", " ", 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"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["195", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02