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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(17/4), 17/4, 5, z] == (1/(555179625 Pi Sqrt[1 + Sqrt[z]] z^4)) (4096 ((-2176 - 2176 Sqrt[z] - 1904 z - 1904 z^(3/2) - 3893 z^2 - 3893 z^(5/2) - 16830 z^3 - 16830 z^(7/2) + 623755 z^4 + 623755 z^(9/2) - 1899128 z^5 - 1899128 z^(11/2) + 2351888 z^6 + 2351888 z^(13/2) - 1345344 z^7 - 1345344 z^(15/2) + 295680 z^8 + 295680 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 8 (-272 - 170 z - 408 z^2 - 1955 z^3 + 44660 z^4 - 127941 z^5 + 153230 z^6 - 85624 z^7 + 18480 z^8) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 17 4 , 17 4 ; 5 ; 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["17", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["17", "4"], 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 555179625 π z + 1 z 4 ( 4096 ( ( 295680 z 17 / 2 + 295680 z 8 - 1345344 z 15 / 2 - 1345344 z 7 + 2351888 z 13 / 2 + 2351888 z 6 - 1899128 z 11 / 2 - 1899128 z 5 + 623755 z 9 / 2 + 623755 z 4 - 16830 z 7 / 2 - 16830 z 3 - 3893 z 5 / 2 - 3893 z 2 - 1904 z 3 / 2 - 1904 z - 2176 z - 2176 ) E ( 2 z z + 1 ) - 8 ( 18480 z 8 - 85624 z 7 + 153230 z 6 - 127941 z 5 + 44660 z 4 - 1955 z 3 - 408 z 2 - 170 z - 272 ) K ( 2 z z + 1 ) ) ) HypergeometricPFQ -1 17 4 17 4 5 z 1 555179625 z 1 2 1 1 2 z 4 -1 4096 295680 z 17 2 295680 z 8 -1 1345344 z 15 2 -1 1345344 z 7 2351888 z 13 2 2351888 z 6 -1 1899128 z 11 2 -1 1899128 z 5 623755 z 9 2 623755 z 4 -1 16830 z 7 2 -1 16830 z 3 -1 3893 z 5 2 -1 3893 z 2 -1 1904 z 3 2 -1 1904 z -1 2176 z 1 2 -2176 EllipticE 2 z 1 2 z 1 2 1 -1 -1 8 18480 z 8 -1 85624 z 7 153230 z 6 -1 127941 z 5 44660 z 4 -1 1955 z 3 -1 408 z 2 -1 170 z -272 EllipticK 2 z 1 2 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02