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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bxp3.01

 Input Form

 Hypergeometric2F1[1/8, 21/8, 4, z] == -((2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-128 + 27 z + 36 z^2) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-128 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) + 3 (25 + 9 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 9 Sqrt[1 - z]) z + (39 + 36 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 36 Sqrt[1 - z]) z^2 + 144 z^3) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (156975 Pi (1 + Sqrt[1 - z])^(1/4) z^3))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 21 8 ; 4 ; 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["21", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["4", 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 156975 π 1 - z + 1 4 z 3 ( 2048 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 36 z 2 + 27 z - 128 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( 144 z 3 + ( 36 2 1 - z 4 1 - z + 1 + 36 1 - z + 39 ) z 2 + 3 ( 9 2 1 - z 4 1 - z + 1 + 9 1 - z + 25 ) z - 128 ( 2 1 - z 4 1 - z + 1 + 1 - z + 1 ) ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) HypergeometricPFQ 1 8 21 8 4 z -1 1 156975 1 -1 z 1 2 1 1 4 z 3 -1 2048 2 1 4 2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 36 z 2 27 z -128 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 144 z 3 36 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 36 1 -1 z 1 2 39 z 2 3 9 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 9 1 -1 z 1 2 25 z -1 128 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 1 -1 z 1 2 1 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["21", "8"], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["2048", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", 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["-", "128"]], "+", RowBox[List["27", " ", "z"]], "+", RowBox[List["36", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "128"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["25", "+", RowBox[List["9", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["9", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["39", "+", RowBox[List["36", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]], "+", RowBox[List["36", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["144", " ", 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["156975", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", "3"]]]]]]]]]]

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

 2007-05-02