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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[5/2, 19/4, 1, z] == (-2 (1 - z)^(3/2) (6008 + 16413 z + 864 z^2 - 80 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 (-1 + z) (6008 + 16413 z + 864 z^2 - 80 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(5/4) (-6008 - 16413 z - 864 z^2 + 80 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/2) (-6008 - 16413 z - 864 z^2 + 80 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-1 + z) (-6008 - 16413 z - 864 z^2 + 80 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (1388 - 12001 z - 13392 z^2 + 880 z^3 - 80 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (1155 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^7)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "2"], ",", FractionBox["19", "4"], ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["6008", "+", RowBox[List["16413", " ", "z"]], "+", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["6008", "+", RowBox[List["16413", " ", "z"]], "+", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["5", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6008"]], "-", RowBox[List["16413", " ", "z"]], "-", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6008"]], "-", RowBox[List["16413", " ", "z"]], "-", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6008"]], "-", RowBox[List["16413", " ", "z"]], "-", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["1388", "-", RowBox[List["12001", " ", "z"]], "-", RowBox[List["13392", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["880", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["1155", " ", SqrtBox["2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 5 2 , 19 4 ; 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["19", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", 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] ( - 2 ( - 80 z 3 + 864 z 2 + 16413 z + 6008 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 - ( 80 z 3 - 864 z 2 - 16413 z - 6008 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 - ( 80 z 3 - 864 z 2 - 16413 z - 6008 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 5 / 4 + ( - 80 z 4 + 880 z 3 - 13392 z 2 - 12001 z + 1388 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 4 + 2 ( z - 1 ) ( - 80 z 3 + 864 z 2 + 16413 z + 6008 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( z - 1 ) ( 80 z 3 - 864 z 2 - 16413 z - 6008 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) / ( 1155 2 π 1 - z + 1 ( z - 1 ) 7 ) HypergeometricPFQ 5 2 19 4 1 z -2 -80 z 3 864 z 2 16413 z 6008 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 -1 80 z 3 -1 864 z 2 -1 16413 z -6008 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 -1 80 z 3 -1 864 z 2 -1 16413 z -6008 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 5 4 -80 z 4 880 z 3 -1 13392 z 2 -1 12001 z 1388 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 2 z -1 -80 z 3 864 z 2 16413 z 6008 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 z -1 80 z 3 -1 864 z 2 -1 16413 z -6008 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1155 2 1 2 1 -1 z 1 2 1 1 2 z -1 7 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "2"], ",", FractionBox["19", "4"], ",", "1", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List["6008", "+", RowBox[List["16413", " ", "z"]], "+", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List["6008", "+", RowBox[List["16413", " ", "z"]], "+", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["5", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6008"]], "-", RowBox[List["16413", " ", "z"]], "-", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6008"]], "-", RowBox[List["16413", " ", "z"]], "-", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6008"]], "-", RowBox[List["16413", " ", "z"]], "-", RowBox[List["864", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List["1388", "-", RowBox[List["12001", " ", "z"]], "-", RowBox[List["13392", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["880", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["80", " ", 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["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]]]], RowBox[List["1155", " ", SqrtBox["2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]]]]]]]

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

 2007-05-02