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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aa5k.01

 Input Form

 Hypergeometric2F1[-(9/2), 19/4, 1, z] == (1/(5544 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])) (2 (33872 - 484160 z + 1779492 z^2 - 2384148 z^3 + 1057485 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (33872 - 484160 z + 1779492 z^2 - 2384148 z^3 + 1057485 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-33872 + 484160 z - 1779492 z^2 + 2384148 z^3 - 1057485 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-33872 + 484160 z - 1779492 z^2 + 2384148 z^3 - 1057485 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-33872 + 484160 z - 1779492 z^2 + 2384148 z^3 - 1057485 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 17 (1 - z)^(3/4) (-688 + 416 z + 32292 z^2 - 90480 z^3 + 62205 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["9", "2"]]], ",", FractionBox["19", "4"], ",", "1", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["5544", " ", SqrtBox["2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["33872", "-", RowBox[List["484160", " ", "z"]], "+", RowBox[List["1779492", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2384148", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1057485", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["33872", "-", RowBox[List["484160", " ", "z"]], "+", RowBox[List["1779492", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2384148", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["1057485", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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[RowBox[List["(", RowBox[List[RowBox[List["-", "33872"]], "+", RowBox[List["484160", " ", "z"]], "-", RowBox[List["1779492", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2384148", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1057485", " ", 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[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33872"]], "+", RowBox[List["484160", " ", "z"]], "-", RowBox[List["1779492", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2384148", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1057485", " ", 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[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "33872"]], "+", RowBox[List["484160", " ", "z"]], "-", RowBox[List["1779492", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2384148", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1057485", " ", 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["17", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "688"]], "+", RowBox[List["416", " ", "z"]], "+", RowBox[List["32292", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["90480", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["62205", " ", 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"]]]]]]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 9 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[RowBox[List["-", FractionBox["9", "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] 1 5544 2 π 1 - z + 1 ( 2 1 - z ( 1057485 z 4 - 2384148 z 3 + 1779492 z 2 - 484160 z + 33872 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 2 ( 1057485 z 4 - 2384148 z 3 + 1779492 z 2 - 484160 z + 33872 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( - 1057485 z 4 + 2384148 z 3 - 1779492 z 2 + 484160 z - 33872 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( - 1057485 z 4 + 2384148 z 3 - 1779492 z 2 + 484160 z - 33872 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( - 1057485 z 4 + 2384148 z 3 - 1779492 z 2 + 484160 z - 33872 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 17 ( 1 - z ) 3 / 4 ( 62205 z 4 - 90480 z 3 + 32292 z 2 + 416 z - 688 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) HypergeometricPFQ -1 9 2 19 4 1 z 1 5544 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 -1 z 1 2 1057485 z 4 -1 2384148 z 3 1779492 z 2 -1 484160 z 33872 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 2 1057485 z 4 -1 2384148 z 3 1779492 z 2 -1 484160 z 33872 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 -1057485 z 4 2384148 z 3 -1 1779492 z 2 484160 z -33872 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 -1057485 z 4 2384148 z 3 -1 1779492 z 2 484160 z -33872 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1057485 z 4 2384148 z 3 -1 1779492 z 2 484160 z -33872 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 17 1 -1 z 3 4 62205 z 4 -1 90480 z 3 32292 z 2 416 z -688 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02