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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.cbj3.01

 Input Form

 Hypergeometric2F1[31/8, 37/8, 4, z] == (1/(6373185 Pi (-1 + z)^5 z^3)) (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-1 + z) (128 - 597 z + 1330 z^2 + 483 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 40 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (2 - 9 z + 175 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (16 - 79 z - 1890 z^2 + 161 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-1 + z) (128 - 597 z + 1330 z^2 + 483 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( 31 8 , 37 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["31", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["37", "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 6373185 π ( z - 1 ) 5 z 3 ( 1024 2 3 / 4 1 - z + 1 4 ( 4 ( z - 1 ) ( 483 z 3 + 1330 z 2 - 597 z + 128 ) E ( 1 2 - 1 2 1 - z + 1 ) - 40 2 1 - z + 1 ( z - 1 ) ( 175 z 2 - 9 z + 2 ) K ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 1 - z ( 161 z 3 - 1890 z 2 - 79 z + 16 ) K ( 1 2 - 1 2 1 - z + 1 ) - 2 ( z - 1 ) ( 483 z 3 + 1330 z 2 - 597 z + 128 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 31 8 37 8 4 z 1 6373185 z -1 5 z 3 -1 1024 2 3 4 1 -1 z 1 2 1 1 4 4 z -1 483 z 3 1330 z 2 -1 597 z 128 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 40 2 1 2 1 -1 z 1 2 1 1 2 z -1 175 z 2 -1 9 z 2 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 2 161 z 3 -1 1890 z 2 -1 79 z 16 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 2 z -1 483 z 3 1330 z 2 -1 597 z 128 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["37", "8"], ",", "4", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["1024", " ", 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["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["128", "-", RowBox[List["597", " ", "z"]], "+", RowBox[List["1330", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["483", " ", 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["40", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["9", " ", "z"]], "+", RowBox[List["175", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", 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["16", "-", RowBox[List["79", " ", "z"]], "-", RowBox[List["1890", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["161", " ", 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["128", "-", RowBox[List["597", " ", "z"]], "+", RowBox[List["1330", " ", 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["6373185", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "5"], " ", SuperscriptBox["z", "3"]]]]]]]]

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

 2007-05-02