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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/8, 29/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1024 + 160 z + 169 z^2 + 240 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1024 + 160 z + 169 z^2 + 240 z^3) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-1024 + 160 z + 169 z^2 + 240 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-512 + 272 z + 107 z^2 + 108 z^3 + 480 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (34063575 Pi (1 + Sqrt[1 - z])^(1/4) z^4)

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 29 8 ; 5 ; 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", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["29", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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 34063575 π 1 - z + 1 4 z 4 ( 65536 2 4 ( - 2 2 1 - z + 1 1 - z 4 ( 240 z 3 + 169 z 2 + 160 z - 1024 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) + 1 - z ( 240 z 3 + 169 z 2 + 160 z - 1024 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) + 2 1 - z + 1 1 - z 4 ( 240 z 3 + 169 z 2 + 160 z - 1024 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) + 2 ( 480 z 4 + 108 z 3 + 107 z 2 + 272 z - 512 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) HypergeometricPFQ 1 8 29 8 5 z 1 34063575 1 -1 z 1 2 1 1 4 z 4 -1 65536 2 1 4 -2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 240 z 3 169 z 2 160 z -1024 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 1 -1 z 1 2 240 z 3 169 z 2 160 z -1024 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 240 z 3 169 z 2 160 z -1024 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 2 480 z 4 108 z 3 107 z 2 272 z -512 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "8"], ",", FractionBox["29", "8"], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["65536", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1024"]], "+", RowBox[List["160", " ", "z"]], "+", RowBox[List["169", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["240", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1024"]], "+", RowBox[List["160", " ", "z"]], "+", RowBox[List["169", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["240", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1024"]], "+", RowBox[List["160", " ", "z"]], "+", RowBox[List["169", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["240", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "512"]], "+", RowBox[List["272", " ", "z"]], "+", RowBox[List["107", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["108", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["480", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["34063575", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", "4"]]]]]]]]

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

 2007-05-02