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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.cb22.01

 Input Form

 Hypergeometric2F1[29/8, 39/8, 3, z] == (1/(973245 Pi (-1 + z)^6 z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-1 + z) (-40 + 385 z + 1894 z^2 + 65 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (5 - 1568 z - 767 z^2 + 26 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-5 - 2485 z - 647 z^2 + 65 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-1 + z) (-40 + 385 z + 1894 z^2 + 65 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( 29 8 , 39 8 ; 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["29", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["39", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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 973245 π ( z - 1 ) 6 z 2 ( 128 2 3 / 4 1 - z + 1 4 ( - 4 ( z - 1 ) ( 65 z 3 + 1894 z 2 + 385 z - 40 ) E ( 1 2 - 1 2 1 - z + 1 ) - 5 2 1 - z + 1 ( z - 1 ) ( 26 z 3 - 767 z 2 - 1568 z + 5 ) K ( 1 2 - 1 2 1 - z + 1 ) - 3 2 1 - z + 1 1 - z ( 65 z 3 - 647 z 2 - 2485 z - 5 ) K ( 1 2 - 1 2 1 - z + 1 ) + 2 ( z - 1 ) ( 65 z 3 + 1894 z 2 + 385 z - 40 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 29 8 39 8 3 z 1 973245 z -1 6 z 2 -1 128 2 3 4 1 -1 z 1 2 1 1 4 -4 z -1 65 z 3 1894 z 2 385 z -40 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 5 2 1 2 1 -1 z 1 2 1 1 2 z -1 26 z 3 -1 767 z 2 -1 1568 z 5 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 3 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 65 z 3 -1 647 z 2 -1 2485 z -5 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 2 z -1 65 z 3 1894 z 2 385 z -40 EllipticK 1 2 -1 1 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["29", "8"], ",", FractionBox["39", "8"], ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["128", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "40"]], "+", RowBox[List["385", " ", "z"]], "+", RowBox[List["1894", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["65", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["5", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["1568", " ", "z"]], "-", RowBox[List["767", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["26", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List["3", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "-", RowBox[List["2485", " ", "z"]], "-", RowBox[List["647", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["65", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "40"]], "+", RowBox[List["385", " ", "z"]], "+", RowBox[List["1894", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["65", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["973245", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"], " ", SuperscriptBox["z", "2"]]]]]]]]

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

 2007-05-02