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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[31/8, 45/8, 5, z] == (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (8 (-1 + z) (1536 - 5968 z + 8485 z^2 - 4830 z^3 + 1449 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (384 - 1429 z + 1906 z^2 + 483 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (384 - 1597 z + 2480 z^2 - 4025 z^3 + 966 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 4 (-1 + z) (1536 - 5968 z + 8485 z^2 - 4830 z^3 + 1449 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (235807845 Pi (-1 + z)^5 z^4)

 Standard Form

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 MathML Form

 2 F 1 ( 31 8 , 45 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["31", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["45", "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 235807845 π ( z - 1 ) 5 z 4 ( 32768 2 3 / 4 1 - z + 1 4 ( 8 ( z - 1 ) ( 1449 z 4 - 4830 z 3 + 8485 z 2 - 5968 z + 1536 ) E ( 1 2 - 1 2 1 - z + 1 ) - 5 2 1 - z + 1 ( z - 1 ) ( 483 z 3 + 1906 z 2 - 1429 z + 384 ) K ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 1 - z ( 966 z 4 - 4025 z 3 + 2480 z 2 - 1597 z + 384 ) K ( 1 2 - 1 2 1 - z + 1 ) - 4 ( z - 1 ) ( 1449 z 4 - 4830 z 3 + 8485 z 2 - 5968 z + 1536 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 31 8 45 8 5 z 1 235807845 z -1 5 z 4 -1 32768 2 3 4 1 -1 z 1 2 1 1 4 8 z -1 1449 z 4 -1 4830 z 3 8485 z 2 -1 5968 z 1536 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 -1 483 z 3 1906 z 2 -1 1429 z 384 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 3 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 966 z 4 -1 4025 z 3 2480 z 2 -1 1597 z 384 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 4 z -1 1449 z 4 -1 4830 z 3 8485 z 2 -1 5968 z 1536 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["31", "8"], ",", FractionBox["45", "8"], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["32768", " ", 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["8", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["1536", "-", RowBox[List["5968", " ", "z"]], "+", RowBox[List["8485", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4830", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1449", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["384", "-", RowBox[List["1429", " ", "z"]], "+", RowBox[List["1906", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["483", " ", 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["384", "-", RowBox[List["1597", " ", "z"]], "+", RowBox[List["2480", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4025", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["966", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["1536", "-", RowBox[List["5968", " ", "z"]], "+", RowBox[List["8485", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4830", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1449", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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["235807845", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"], " ", SuperscriptBox["z", "4"]]]]]]]]

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

 2007-05-02