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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9518.01

 Input Form

 HypergeometricPFQ[{-(7/2), 3, 4}, {-(1/2), 7/2}, -z] == (1/(4194304 z^2)) (-53760 - 44800 z + 3695232 z^2 - 88820928 z^3 - 46305000 Pi^2 z^(7/2) - 594732600 z^4 - 183367800 Pi^2 z^(9/2) - 624323700 z^5 - 156080925 Pi^2 z^(11/2)) + (1/(150994944 (1 + z)^(23/2))) ((-144916480 + 30290411520 z - 135324129920 z^2 + 4283020138880 z^3 + 15207858687280 z^4 + 57628171476512 z^5 + 141752299247440 z^6 + 256079048474660 z^7 + 345798310748770 z^8 + 352210947836335 z^9 + 270040450579837 z^10 + 153727155174600 z^11 + 63106173635400 z^12 + 17680088344275 z^13 + 3028805688825 z^14 + 239553253170 z^15) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(150994944 (1 + z)^(23/2))) ((144916480 - 30290411520 z + 135324129920 z^2 - 4283020138880 z^3 - 15207858687280 z^4 - 57628171476512 z^5 - 141752299247440 z^6 - 256079048474660 z^7 - 345798310748770 z^8 - 352210947836335 z^9 - 270040450579837 z^10 - 153727155174600 z^11 - 63106173635400 z^12 - 17680088344275 z^13 - 3028805688825 z^14 - 239553253170 z^15) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (1/(1048576 z^(5/2) Sqrt[1 + z])) (105 (-128 - 192 z - 1248 z^2 + 27408 z^3 + 824922 z^4 + 2241855 z^5 + 1486485 z^6) Log[Sqrt[z] + Sqrt[1 + z]]) + (1/(150994944 (1 + z)^(23/2))) ((144916480 - 30290411520 z + 135324129920 z^2 - 4283020138880 z^3 - 15207858687280 z^4 - 57628171476512 z^5 - 141752299247440 z^6 - 256079048474660 z^7 - 345798310748770 z^8 - 352210947836335 z^9 - 270040450579837 z^10 - 153727155174600 z^11 - 63106173635400 z^12 - 17680088344275 z^13 - 3028805688825 z^14 - 239553253170 z^15) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (33075 z^(3/2) (1400 + 5544 z + 4719 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/1048576 - (33075 z^(3/2) (1400 + 5544 z + 4719 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/1048576 + (33075 z^(3/2) (1400 + 5544 z + 4719 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/1048576

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 3 , 4 ; - 1 2 , 7 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "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] - 33075 ( 4719 z 2 + 5544 z + 1400 ) log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) z 3 / 2 1048576 - 33075 ( 4719 z 2 + 5544 z + 1400 ) Li PolyLog 2 ( - 1 z + z + 1 ) z 3 / 2 1048576 + 33075 ( 4719 z 2 + 5544 z + 1400 ) Li PolyLog 2 ( 1 z + z + 1 ) z 3 / 2 1048576 + 1 150994944 ( z + 1 ) 23 / 2 ( ( 239553253170 z 15 + 3028805688825 z 14 + 17680088344275 z 13 + 63106173635400 z 12 + 153727155174600 z 11 + 270040450579837 z 10 + 352210947836335 z 9 + 345798310748770 z 8 + 256079048474660 z 7 + 141752299247440 z 6 + 57628171476512 z 5 + 15207858687280 z 4 + 4283020138880 z 3 - 135324129920 z 2 + 30290411520 z - 144916480 ) log ( z - z + 1 + 1 ) ) + 1 150994944 ( z + 1 ) 23 / 2 ( ( - 239553253170 z 15 - 3028805688825 z 14 - 17680088344275 z 13 - 63106173635400 z 12 - 153727155174600 z 11 - 270040450579837 z 10 - 352210947836335 z 9 - 345798310748770 z 8 - 256079048474660 z 7 - 141752299247440 z 6 - 57628171476512 z 5 - 15207858687280 z 4 - 4283020138880 z 3 + 135324129920 z 2 - 30290411520 z + 144916480 ) log ( - z + z + 1 + 1 ) ) + 1 150994944 ( z + 1 ) 23 / 2 ( ( - 239553253170 z 15 - 3028805688825 z 14 - 17680088344275 z 13 - 63106173635400 z 12 - 153727155174600 z 11 - 270040450579837 z 10 - 352210947836335 z 9 - 345798310748770 z 8 - 256079048474660 z 7 - 141752299247440 z 6 - 57628171476512 z 5 - 15207858687280 z 4 - 4283020138880 z 3 + 135324129920 z 2 - 30290411520 z + 144916480 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) ) + 1 4194304 z 2 ( - 156080925 π 2 z 11 / 2 - 624323700 z 5 - 183367800 π 2 z 9 / 2 - 594732600 z 4 - 46305000 π 2 z 7 / 2 - 88820928 z 3 + 3695232 z 2 - 44800 z - 53760 ) - 1 1048576 z + 1 z 5 / 2 105 ( 1486485 z 6 + 2241855 z 5 + 824922 z 4 + 27408 z 3 - 1248 z 2 - 192 z - 128 ) log ( z + z + 1 ) HypergeometricPFQ -1 7 2 3 4 -1 1 2 7 2 -1 z -1 33075 4719 z 2 5544 z 1400 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 z 3 2 1048576 -1 -1 33075 4719 z 2 5544 z 1400 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 z 3 2 1048576 -1 33075 4719 z 2 5544 z 1400 PolyLog 2 1 z 1 2 z 1 1 2 -1 z 3 2 1048576 -1 1 150994944 z 1 23 2 -1 239553253170 z 15 3028805688825 z 14 17680088344275 z 13 63106173635400 z 12 153727155174600 z 11 270040450579837 z 10 352210947836335 z 9 345798310748770 z 8 256079048474660 z 7 141752299247440 z 6 57628171476512 z 5 15207858687280 z 4 4283020138880 z 3 -1 135324129920 z 2 30290411520 z -144916480 z 1 2 -1 z 1 1 2 1 1 150994944 z 1 23 2 -1 -239553253170 z 15 -1 3028805688825 z 14 -1 17680088344275 z 13 -1 63106173635400 z 12 -1 153727155174600 z 11 -1 270040450579837 z 10 -1 352210947836335 z 9 -1 345798310748770 z 8 -1 256079048474660 z 7 -1 141752299247440 z 6 -1 57628171476512 z 5 -1 15207858687280 z 4 -1 4283020138880 z 3 135324129920 z 2 -1 30290411520 z 144916480 -1 z 1 2 z 1 1 2 1 1 150994944 z 1 23 2 -1 -239553253170 z 15 -1 3028805688825 z 14 -1 17680088344275 z 13 -1 63106173635400 z 12 -1 153727155174600 z 11 -1 270040450579837 z 10 -1 352210947836335 z 9 -1 345798310748770 z 8 -1 256079048474660 z 7 -1 141752299247440 z 6 -1 57628171476512 z 5 -1 15207858687280 z 4 -1 4283020138880 z 3 135324129920 z 2 -1 30290411520 z 144916480 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 1 4194304 z 2 -1 -156080925 2 z 11 2 -1 624323700 z 5 -1 183367800 2 z 9 2 -1 594732600 z 4 -1 46305000 2 z 7 2 -1 88820928 z 3 3695232 z 2 -1 44800 z -53760 -1 1 1048576 z 1 1 2 z 5 2 -1 105 1486485 z 6 2241855 z 5 824922 z 4 27408 z 3 -1 1248 z 2 -1 192 z -128 z 1 2 z 1 1 2 [/itex]

 Rule Form

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

 2007-05-02