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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.av0r.01

 Input Form

 HypergeometricPFQ[{3, 7/2, 4}, {-(5/2), -(3/2)}, -z] == (1/(640 (1 + z)^14)) (640 + 1792 z + 387968 z^2 + 100219392 z^3 - 6487306112 z^4 + 62757199232 z^5 - 182482203904 z^6 + 191542672464 z^7 - 74033643684 z^8 + 9386028729 z^9 - 267824634 z^10 + 194040 z^11) + (9009 (-16896 z^(7/2) + 395648 z^(9/2) - 2265216 z^(11/2) + 4499440 z^(13/2) - 3436620 z^(15/2) + 991683 z^(17/2) - 93324 z^(19/2) + 1848 z^(21/2)) ArcSinh[Sqrt[z]])/(128 Sqrt[1 + z] (1 + 14 z + 91 z^2 + 364 z^3 + 1001 z^4 + 2002 z^5 + 3003 z^6 + 3432 z^7 + 3003 z^8 + 2002 z^9 + 1001 z^10 + 364 z^11 + 91 z^12 + 14 z^13 + z^14))

 Standard Form

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 MathML Form

 3 F 2 ( 3 , 7 2 , 4 ; - 5 2 , - 3 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["3", "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] 1 640 ( z + 1 ) 14 ( 194040 z 11 - 267824634 z 10 + 9386028729 z 9 - 74033643684 z 8 + 191542672464 z 7 - 182482203904 z 6 + 62757199232 z 5 - 6487306112 z 4 + 100219392 z 3 + 387968 z 2 + 1792 z + 640 ) + ( 9009 ( 1848 z 21 / 2 - 93324 z 19 / 2 + 991683 z 17 / 2 - 3436620 z 15 / 2 + 4499440 z 13 / 2 - 2265216 z 11 / 2 + 395648 z 9 / 2 - 16896 z 7 / 2 ) sinh - 1 ( z ) ) / ( 128 z + 1 ( z 14 + 14 z 13 + 91 z 12 + 364 z 11 + 1001 z 10 + 2002 z 9 + 3003 z 8 + 3432 z 7 + 3003 z 6 + 2002 z 5 + 1001 z 4 + 364 z 3 + 91 z 2 + 14 z + 1 ) ) HypergeometricPFQ 3 7 2 4 -1 5 2 -1 3 2 -1 z 1 640 z 1 14 -1 194040 z 11 -1 267824634 z 10 9386028729 z 9 -1 74033643684 z 8 191542672464 z 7 -1 182482203904 z 6 62757199232 z 5 -1 6487306112 z 4 100219392 z 3 387968 z 2 1792 z 640 9009 1848 z 21 2 -1 93324 z 19 2 991683 z 17 2 -1 3436620 z 15 2 4499440 z 13 2 -1 2265216 z 11 2 395648 z 9 2 -1 16896 z 7 2 z 1 2 128 z 1 1 2 z 14 14 z 13 91 z 12 364 z 11 1001 z 10 2002 z 9 3003 z 8 3432 z 7 3003 z 6 2002 z 5 1001 z 4 364 z 3 91 z 2 14 z 1 -1 [/itex]

 Rule Form

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

 2007-05-02