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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9920.01

 Input Form

 HypergeometricPFQ[{-(7/2), 4, 4}, {3/2, 5/2}, -z] == (1/(167772160 z)) (3 (17920 + 560000 Pi^2 Sqrt[z] + 45598400 z + 27440000 Pi^2 z^(3/2) + 505048096 z^2 + 185220000 Pi^2 z^(5/2) + 1293707800 z^3 + 373527000 Pi^2 z^(7/2) + 901800900 z^4 + 225450225 Pi^2 z^(9/2))) + (1/(629145600 (1 + z)^(19/2))) ((-1136556672 - 26698781824 z - 266140595552 z^2 - 1451188470280 z^3 - 5093254036259 z^4 - 12330063689380 z^5 - 21411264010763 z^6 - 27191711657182 z^7 - 25377379426250 z^8 - 17250595688230 z^9 - 8323826592375 z^10 - 2705375584170 z^11 - 531706027545 z^12 - 47786889150 z^13) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(629145600 (1 + z)^(19/2))) ((1136556672 + 26698781824 z + 266140595552 z^2 + 1451188470280 z^3 + 5093254036259 z^4 + 12330063689380 z^5 + 21411264010763 z^6 + 27191711657182 z^7 + 25377379426250 z^8 + 17250595688230 z^9 + 8323826592375 z^10 + 2705375584170 z^11 + 531706027545 z^12 + 47786889150 z^13) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (1/(8388608 z^(3/2) Sqrt[1 + z])) (7 (-384 + 173008 z + 4847448 z^2 + 23971626 z^3 + 38458035 z^4 + 19324305 z^5) Log[Sqrt[z] + Sqrt[1 + z]]) + (1/(629145600 (1 + z)^(19/2))) ((1136556672 + 26698781824 z + 266140595552 z^2 + 1451188470280 z^3 + 5093254036259 z^4 + 12330063689380 z^5 + 21411264010763 z^6 + 27191711657182 z^7 + 25377379426250 z^8 + 17250595688230 z^9 + 8323826592375 z^10 + 2705375584170 z^11 + 531706027545 z^12 + 47786889150 z^13) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (1/(8388608 Sqrt[z])) (105 (3200 + 156800 z + 1058400 z^2 + 2134440 z^3 + 1288287 z^4) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (1/(8388608 Sqrt[z])) (105 (3200 + 156800 z + 1058400 z^2 + 2134440 z^3 + 1288287 z^4) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))]) - (1/(8388608 Sqrt[z])) (105 (3200 + 156800 z + 1058400 z^2 + 2134440 z^3 + 1288287 z^4) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 4 , 4 ; 3 2 , 5 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["4", 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[FractionBox["3", "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[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 167772160 z ( 3 ( 225450225 π 2 z 9 / 2 + 901800900 z 4 + 373527000 π 2 z 7 / 2 + 1293707800 z 3 + 185220000 π 2 z 5 / 2 + 505048096 z 2 + 27440000 π 2 z 3 / 2 + 45598400 z + 560000 π 2 z + 17920 ) ) + 1 629145600 ( z + 1 ) 19 / 2 ( ( - 47786889150 z 13 - 531706027545 z 12 - 2705375584170 z 11 - 8323826592375 z 10 - 17250595688230 z 9 - 25377379426250 z 8 - 27191711657182 z 7 - 21411264010763 z 6 - 12330063689380 z 5 - 5093254036259 z 4 - 1451188470280 z 3 - 266140595552 z 2 - 26698781824 z - 1136556672 ) log ( z - z + 1 + 1 ) ) + 1 629145600 ( z + 1 ) 19 / 2 ( ( 47786889150 z 13 + 531706027545 z 12 + 2705375584170 z 11 + 8323826592375 z 10 + 17250595688230 z 9 + 25377379426250 z 8 + 27191711657182 z 7 + 21411264010763 z 6 + 12330063689380 z 5 + 5093254036259 z 4 + 1451188470280 z 3 + 266140595552 z 2 + 26698781824 z + 1136556672 ) log ( - z + z + 1 + 1 ) ) + 1 8388608 z 3 / 2 z + 1 7 ( 19324305 z 5 + 38458035 z 4 + 23971626 z 3 + 4847448 z 2 + 173008 z - 384 ) log ( z + z + 1 ) + 1 629145600 ( z + 1 ) 19 / 2 ( ( 47786889150 z 13 + 531706027545 z 12 + 2705375584170 z 11 + 8323826592375 z 10 + 17250595688230 z 9 + 25377379426250 z 8 + 27191711657182 z 7 + 21411264010763 z 6 + 12330063689380 z 5 + 5093254036259 z 4 + 1451188470280 z 3 + 266140595552 z 2 + 26698781824 z + 1136556672 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) ) + 1 8388608 z 105 ( 1288287 z 4 + 2134440 z 3 + 1058400 z 2 + 156800 z + 3200 ) log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) + 105 ( 1288287 z 4 + 2134440 z 3 + 1058400 z 2 + 156800 z + 3200 ) Li PolyLog 2 ( - 1 z + z + 1 ) 8388608 z - 105 ( 1288287 z 4 + 2134440 z 3 + 1058400 z 2 + 156800 z + 3200 ) Li PolyLog 2 ( 1 z + z + 1 ) 8388608 z HypergeometricPFQ -1 7 2 4 4 3 2 5 2 -1 z 1 167772160 z -1 3 225450225 2 z 9 2 901800900 z 4 373527000 2 z 7 2 1293707800 z 3 185220000 2 z 5 2 505048096 z 2 27440000 2 z 3 2 45598400 z 560000 2 z 1 2 17920 1 629145600 z 1 19 2 -1 -47786889150 z 13 -1 531706027545 z 12 -1 2705375584170 z 11 -1 8323826592375 z 10 -1 17250595688230 z 9 -1 25377379426250 z 8 -1 27191711657182 z 7 -1 21411264010763 z 6 -1 12330063689380 z 5 -1 5093254036259 z 4 -1 1451188470280 z 3 -1 266140595552 z 2 -1 26698781824 z -1136556672 z 1 2 -1 z 1 1 2 1 1 629145600 z 1 19 2 -1 47786889150 z 13 531706027545 z 12 2705375584170 z 11 8323826592375 z 10 17250595688230 z 9 25377379426250 z 8 27191711657182 z 7 21411264010763 z 6 12330063689380 z 5 5093254036259 z 4 1451188470280 z 3 266140595552 z 2 26698781824 z 1136556672 -1 z 1 2 z 1 1 2 1 1 8388608 z 3 2 z 1 1 2 -1 7 19324305 z 5 38458035 z 4 23971626 z 3 4847448 z 2 173008 z -384 z 1 2 z 1 1 2 1 629145600 z 1 19 2 -1 47786889150 z 13 531706027545 z 12 2705375584170 z 11 8323826592375 z 10 17250595688230 z 9 25377379426250 z 8 27191711657182 z 7 21411264010763 z 6 12330063689380 z 5 5093254036259 z 4 1451188470280 z 3 266140595552 z 2 26698781824 z 1136556672 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 1 8388608 z 1 2 -1 105 1288287 z 4 2134440 z 3 1058400 z 2 156800 z 3200 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 105 1288287 z 4 2134440 z 3 1058400 z 2 156800 z 3200 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 8388608 z 1 2 -1 -1 105 1288287 z 4 2134440 z 3 1058400 z 2 156800 z 3200 PolyLog 2 1 z 1 2 z 1 1 2 -1 8388608 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02