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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.atyf.01

 Input Form

 HypergeometricPFQ[{5/2, 5/2, 5/2}, {-(7/2), 1}, -z] == (1/(105 Pi (1 + z)^10)) (4 (122 + 1687 z + 12312 z^2 + 74050 z^3 + 845750 z^4 - 1959633 z^5 + 668672 z^6 - 29888 z^7) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(105 Pi (1 + z)^(19/2))) (4 (122 + 1687 z + 12312 z^2 + 74050 z^3 + 845750 z^4 - 1959633 z^5 + 668672 z^6 - 29888 z^7) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(105 Pi z (1 + z)^9)) (4 (-105 - 1562 z - 11934 z^2 - 70680 z^3 - 607345 z^4 + 2011770 z^5 - 837312 z^6 + 44416 z^7) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(105 Pi z (1 + z)^(19/2))) (4 (105 + 1423 z + 10122 z^2 + 57990 z^3 + 529925 z^4 - 3095925 z^5 + 2744808 z^6 - 544448 z^7 + 15360 z^8) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

 Standard Form

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 MathML Form

 3 F 2 ( 5 2 , 5 2 , 5 2 ; - 7 2 , 1 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 105 π ( z + 1 ) 19 / 2 4 ( - 29888 z 7 + 668672 z 6 - 1959633 z 5 + 845750 z 4 + 74050 z 3 + 12312 z 2 + 1687 z + 122 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 105 π ( z + 1 ) 10 4 ( - 29888 z 7 + 668672 z 6 - 1959633 z 5 + 845750 z 4 + 74050 z 3 + 12312 z 2 + 1687 z + 122 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 105 π z ( z + 1 ) 9 4 ( 44416 z 7 - 837312 z 6 + 2011770 z 5 - 607345 z 4 - 70680 z 3 - 11934 z 2 - 1562 z - 105 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 105 π z ( z + 1 ) 19 / 2 ( 4 ( 15360 z 8 - 544448 z 7 + 2744808 z 6 - 3095925 z 5 + 529925 z 4 + 57990 z 3 + 10122 z 2 + 1423 z + 105 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) ) HypergeometricPFQ 5 2 5 2 5 2 -1 7 2 1 -1 z 1 105 z 1 19 2 -1 4 -29888 z 7 668672 z 6 -1 1959633 z 5 845750 z 4 74050 z 3 12312 z 2 1687 z 122 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 105 z 1 10 -1 4 -29888 z 7 668672 z 6 -1 1959633 z 5 845750 z 4 74050 z 3 12312 z 2 1687 z 122 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 105 z z 1 9 -1 4 44416 z 7 -1 837312 z 6 2011770 z 5 -1 607345 z 4 -1 70680 z 3 -1 11934 z 2 -1 1562 z -105 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 105 z z 1 19 2 -1 4 15360 z 8 -1 544448 z 7 2744808 z 6 -1 3095925 z 5 529925 z 4 57990 z 3 10122 z 2 1423 z 105 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02