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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9215.01

 Input Form

 HypergeometricPFQ[{-(7/2), 3, 3}, {-(5/2), 3/2}, -z] == (1/(163840 (1 + z)^3)) (143680 - 605856 z + 2544872 z^2 - 28239948 z^3 - 12006225 Pi^2 z^(7/2) - 117180756 z^4 - 36018675 Pi^2 z^(9/2) - 133402500 z^5 - 36018675 Pi^2 z^(11/2) - 48024900 z^6 - 12006225 Pi^2 z^(13/2)) + (1/(15728640 (1 + z)^(21/2))) ((-15728640 + 29385216 z + 96945408 z^2 + 5493170368 z^3 + 79972349856 z^4 + 555855253800 z^5 + 1977852633596 z^6 + 4505997765048 z^7 + 6994545355833 z^8 + 7621179557761 z^9 + 5858778243465 z^10 + 3123962361135 z^11 + 1102622302530 z^12 + 232185388680 z^13 + 22121058960 z^14) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(15728640 (1 + z)^(21/2))) ((15728640 - 29385216 z - 96945408 z^2 - 5493170368 z^3 - 79972349856 z^4 - 555855253800 z^5 - 1977852633596 z^6 - 4505997765048 z^7 - 6994545355833 z^8 - 7621179557761 z^9 - 5858778243465 z^10 - 3123962361135 z^11 - 1102622302530 z^12 - 232185388680 z^13 - 22121058960 z^14) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (1/(8192 Sqrt[z] (1 + z)^(7/2))) (21 (-48 + 632 z - 2310 z^2 + 12705 z^3 + 191664 z^4 + 442134 z^5 + 381150 z^6 + 114345 z^7) Log[Sqrt[z] + Sqrt[1 + z]]) + (1/(15728640 (1 + z)^(21/2))) ((15728640 - 29385216 z - 96945408 z^2 - 5493170368 z^3 - 79972349856 z^4 - 555855253800 z^5 - 1977852633596 z^6 - 4505997765048 z^7 - 6994545355833 z^8 - 7621179557761 z^9 - 5858778243465 z^10 - 3123962361135 z^11 - 1102622302530 z^12 - 232185388680 z^13 - 22121058960 z^14) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (2401245 z^(7/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/8192 - (2401245 z^(7/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/8192 + (2401245 z^(7/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/8192

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 3 , 3 ; - 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[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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[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] - 2401245 log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) z 7 / 2 8192 - 2401245 Li PolyLog 2 ( - 1 z + z + 1 ) z 7 / 2 8192 + 2401245 Li PolyLog 2 ( 1 z + z + 1 ) z 7 / 2 8192 + 1 163840 ( z + 1 ) 3 ( - 12006225 π 2 z 13 / 2 - 48024900 z 6 - 36018675 π 2 z 11 / 2 - 133402500 z 5 - 36018675 π 2 z 9 / 2 - 117180756 z 4 - 12006225 π 2 z 7 / 2 - 28239948 z 3 + 2544872 z 2 - 605856 z + 143680 ) + 1 15728640 ( z + 1 ) 21 / 2 ( ( 22121058960 z 14 + 232185388680 z 13 + 1102622302530 z 12 + 3123962361135 z 11 + 5858778243465 z 10 + 7621179557761 z 9 + 6994545355833 z 8 + 4505997765048 z 7 + 1977852633596 z 6 + 555855253800 z 5 + 79972349856 z 4 + 5493170368 z 3 + 96945408 z 2 + 29385216 z - 15728640 ) log ( z - z + 1 + 1 ) ) + 1 15728640 ( z + 1 ) 21 / 2 ( ( - 22121058960 z 14 - 232185388680 z 13 - 1102622302530 z 12 - 3123962361135 z 11 - 5858778243465 z 10 - 7621179557761 z 9 - 6994545355833 z 8 - 4505997765048 z 7 - 1977852633596 z 6 - 555855253800 z 5 - 79972349856 z 4 - 5493170368 z 3 - 96945408 z 2 - 29385216 z + 15728640 ) log ( - z + z + 1 + 1 ) ) + 1 15728640 ( z + 1 ) 21 / 2 ( ( - 22121058960 z 14 - 232185388680 z 13 - 1102622302530 z 12 - 3123962361135 z 11 - 5858778243465 z 10 - 7621179557761 z 9 - 6994545355833 z 8 - 4505997765048 z 7 - 1977852633596 z 6 - 555855253800 z 5 - 79972349856 z 4 - 5493170368 z 3 - 96945408 z 2 - 29385216 z + 15728640 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) ) - 1 8192 ( z + 1 ) 7 / 2 z 21 ( 114345 z 7 + 381150 z 6 + 442134 z 5 + 191664 z 4 + 12705 z 3 - 2310 z 2 + 632 z - 48 ) log ( z + z + 1 ) HypergeometricPFQ -1 7 2 3 3 -1 5 2 3 2 -1 z -1 2401245 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 7 2 8192 -1 -1 2401245 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 z 7 2 8192 -1 2401245 PolyLog 2 1 z 1 2 z 1 1 2 -1 z 7 2 8192 -1 1 163840 z 1 3 -1 -12006225 2 z 13 2 -1 48024900 z 6 -1 36018675 2 z 11 2 -1 133402500 z 5 -1 36018675 2 z 9 2 -1 117180756 z 4 -1 12006225 2 z 7 2 -1 28239948 z 3 2544872 z 2 -1 605856 z 143680 1 15728640 z 1 21 2 -1 22121058960 z 14 232185388680 z 13 1102622302530 z 12 3123962361135 z 11 5858778243465 z 10 7621179557761 z 9 6994545355833 z 8 4505997765048 z 7 1977852633596 z 6 555855253800 z 5 79972349856 z 4 5493170368 z 3 96945408 z 2 29385216 z -15728640 z 1 2 -1 z 1 1 2 1 1 15728640 z 1 21 2 -1 -22121058960 z 14 -1 232185388680 z 13 -1 1102622302530 z 12 -1 3123962361135 z 11 -1 5858778243465 z 10 -1 7621179557761 z 9 -1 6994545355833 z 8 -1 4505997765048 z 7 -1 1977852633596 z 6 -1 555855253800 z 5 -1 79972349856 z 4 -1 5493170368 z 3 -1 96945408 z 2 -1 29385216 z 15728640 -1 z 1 2 z 1 1 2 1 1 15728640 z 1 21 2 -1 -22121058960 z 14 -1 232185388680 z 13 -1 1102622302530 z 12 -1 3123962361135 z 11 -1 5858778243465 z 10 -1 7621179557761 z 9 -1 6994545355833 z 8 -1 4505997765048 z 7 -1 1977852633596 z 6 -1 555855253800 z 5 -1 79972349856 z 4 -1 5493170368 z 3 -1 96945408 z 2 -1 29385216 z 15728640 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 -1 1 8192 z 1 7 2 z 1 2 -1 21 114345 z 7 381150 z 6 442134 z 5 191664 z 4 12705 z 3 -1 2310 z 2 632 z -48 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