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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.av0d.01

 Input Form

 HypergeometricPFQ[{3, 7/2, 4}, {-(7/2), 1/2}, -z] == (1/(128 (1 + z)^13)) (128 + 4736 z + 86784 z^2 + 1296128 z^3 + 31960448 z^4 - 354958032 z^5 + 740222184 z^6 - 459461430 z^7 + 84482373 z^8 - 3322578 z^9 + 3432 z^10) + (45045 (-2288 z^(9/2) + 11544 z^(11/2) - 15570 z^(13/2) + 6819 z^(15/2) - 900 z^(17/2) + 24 z^(19/2)) ArcSinh[Sqrt[z]])/ (128 Sqrt[1 + z] (1 + 13 z + 78 z^2 + 286 z^3 + 715 z^4 + 1287 z^5 + 1716 z^6 + 1716 z^7 + 1287 z^8 + 715 z^9 + 286 z^10 + 78 z^11 + 13 z^12 + z^13))

 Standard Form

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 MathML Form

 3 F 2 ( 3 , 7 2 , 4 ; - 7 2 , 1 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", 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[FractionBox["1", "2"], 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] 1 128 ( z + 1 ) 13 ( 3432 z 10 - 3322578 z 9 + 84482373 z 8 - 459461430 z 7 + 740222184 z 6 - 354958032 z 5 + 31960448 z 4 + 1296128 z 3 + 86784 z 2 + 4736 z + 128 ) + ( 45045 ( 24 z 19 / 2 - 900 z 17 / 2 + 6819 z 15 / 2 - 15570 z 13 / 2 + 11544 z 11 / 2 - 2288 z 9 / 2 ) sinh - 1 ( z ) ) / ( 128 z + 1 ( z 13 + 13 z 12 + 78 z 11 + 286 z 10 + 715 z 9 + 1287 z 8 + 1716 z 7 + 1716 z 6 + 1287 z 5 + 715 z 4 + 286 z 3 + 78 z 2 + 13 z + 1 ) ) HypergeometricPFQ 3 7 2 4 -1 7 2 1 2 -1 z 1 128 z 1 13 -1 3432 z 10 -1 3322578 z 9 84482373 z 8 -1 459461430 z 7 740222184 z 6 -1 354958032 z 5 31960448 z 4 1296128 z 3 86784 z 2 4736 z 128 45045 24 z 19 2 -1 900 z 17 2 6819 z 15 2 -1 15570 z 13 2 11544 z 11 2 -1 2288 z 9 2 z 1 2 128 z 1 1 2 z 13 13 z 12 78 z 11 286 z 10 715 z 9 1287 z 8 1716 z 7 1716 z 6 1287 z 5 715 z 4 286 z 3 78 z 2 13 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02