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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9547.01

 Input Form

 HypergeometricPFQ[{-(7/2), 3, 4}, {3/2, 3/2}, z] == (1/(8388608 Sqrt[z])) (3 I (22400 Pi^2 - 2356416 I Sqrt[z] - 1568000 Pi^2 z + 32644192 I z^(3/2) + 12348000 Pi^2 z^2 - 93247000 I z^(5/2) - 27165600 Pi^2 z^3 + 69369300 I z^(7/2) + 17342325 Pi^2 z^4)) - (35 Sqrt[1 - z] (7504 - 289992 z + 1636362 z^2 - 2823975 z^3 + 1486485 z^4) ArcSin[Sqrt[z]])/(2097152 (-1 + z) Sqrt[z]) + (1/(6291456 (-1 + z)^8)) (Sqrt[1 - z] (-6089856 + 204516352 z - 2005107360 z^2 + 10073436320 z^3 - 30722672675 z^4 + 61652943606 z^5 - 84520193372 z^6 + 80008283500 z^7 - 51618596400 z^8 + 21725403525 z^9 - 5388433785 z^10 + 598311945 z^11) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(6291456 (-1 + z)^8)) (Sqrt[1 - z] (6089856 - 204516352 z + 2005107360 z^2 - 10073436320 z^3 + 30722672675 z^4 - 61652943606 z^5 + 84520193372 z^6 - 80008283500 z^7 + 51618596400 z^8 - 21725403525 z^9 + 5388433785 z^10 - 598311945 z^11) Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))]) + (1/(2097152 Sqrt[z])) (525 (128 - 8960 z + 70560 z^2 - 155232 z^3 + 99099 z^4) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) - (1/(6291456 (-1 + z)^8)) (Sqrt[1 - z] (-6089856 + 204516352 z - 2005107360 z^2 + 10073436320 z^3 - 30722672675 z^4 + 61652943606 z^5 - 84520193372 z^6 + 80008283500 z^7 - 51618596400 z^8 + 21725403525 z^9 - 5388433785 z^10 + 598311945 z^11) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (525 I (128 - 8960 z + 70560 z^2 - 155232 z^3 + 99099 z^4) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(2097152 Sqrt[z]) - (525 I (128 - 8960 z + 70560 z^2 - 155232 z^3 + 99099 z^4) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(2097152 Sqrt[z])

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 3 , 4 ; 3 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["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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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 8388608 z ( 3 ( 17342325 π 2 z 4 + 69369300 z 7 / 2 - 27165600 π 2 z 3 - 93247000 z 5 / 2 + 12348000 π 2 z 2 + 32644192 z 3 / 2 - 1568000 π 2 z - 2356416 z + 22400 π 2 ) ) - 35 1 - z ( 1486485 z 4 - 2823975 z 3 + 1636362 z 2 - 289992 z + 7504 ) sin - 1 ( z ) 2097152 ( z - 1 ) z + 1 6291456 ( z - 1 ) 8 ( 1 - z ( 598311945 z 11 - 5388433785 z 10 + 21725403525 z 9 - 51618596400 z 8 + 80008283500 z 7 - 84520193372 z 6 + 61652943606 z 5 - 30722672675 z 4 + 10073436320 z 3 - 2005107360 z 2 + 204516352 z - 6089856 ) log ( 1 - sin - 1 ( z ) ) ) + 1 6291456 ( z - 1 ) 8 ( 1 - z ( - 598311945 z 11 + 5388433785 z 10 - 21725403525 z 9 + 51618596400 z 8 - 80008283500 z 7 + 84520193372 z 6 - 61652943606 z 5 + 30722672675 z 4 - 10073436320 z 3 + 2005107360 z 2 - 204516352 z + 6089856 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) ) + 525 ( 99099 z 4 - 155232 z 3 + 70560 z 2 - 8960 z + 128 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 2097152 z - 1 6291456 ( z - 1 ) 8 ( 1 - z ( 598311945 z 11 - 5388433785 z 10 + 21725403525 z 9 - 51618596400 z 8 + 80008283500 z 7 - 84520193372 z 6 + 61652943606 z 5 - 30722672675 z 4 + 10073436320 z 3 - 2005107360 z 2 + 204516352 z - 6089856 ) log ( 1 + sin - 1 ( z ) ) ) + 525 ( 99099 z 4 - 155232 z 3 + 70560 z 2 - 8960 z + 128 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 2097152 z - 525 ( 99099 z 4 - 155232 z 3 + 70560 z 2 - 8960 z + 128 ) Li PolyLog 2 ( sin - 1 ( z ) ) 2097152 z HypergeometricPFQ -1 7 2 3 4 3 2 3 2 z 1 8388608 z 1 2 -1 3 17342325 2 z 4 69369300 z 7 2 -1 27165600 2 z 3 -1 93247000 z 5 2 12348000 2 z 2 32644192 z 3 2 -1 1568000 2 z -1 2356416 z 1 2 22400 2 -1 35 1 -1 z 1 2 1486485 z 4 -1 2823975 z 3 1636362 z 2 -1 289992 z 7504 z 1 2 2097152 z -1 z 1 2 -1 1 6291456 z -1 8 -1 1 -1 z 1 2 598311945 z 11 -1 5388433785 z 10 21725403525 z 9 -1 51618596400 z 8 80008283500 z 7 -1 84520193372 z 6 61652943606 z 5 -1 30722672675 z 4 10073436320 z 3 -1 2005107360 z 2 204516352 z -6089856 1 -1 z 1 2 1 6291456 z -1 8 -1 1 -1 z 1 2 -598311945 z 11 5388433785 z 10 -1 21725403525 z 9 51618596400 z 8 -1 80008283500 z 7 84520193372 z 6 -1 61652943606 z 5 30722672675 z 4 -1 10073436320 z 3 2005107360 z 2 -1 204516352 z 6089856 1 -1 z 1 2 1 z 1 2 -1 525 99099 z 4 -1 155232 z 3 70560 z 2 -1 8960 z 128 z 1 2 1 -1 z 1 2 1 z 1 2 -1 2097152 z 1 2 -1 -1 1 6291456 z -1 8 -1 1 -1 z 1 2 598311945 z 11 -1 5388433785 z 10 21725403525 z 9 -1 51618596400 z 8 80008283500 z 7 -1 84520193372 z 6 61652943606 z 5 -1 30722672675 z 4 10073436320 z 3 -1 2005107360 z 2 204516352 z -6089856 1 z 1 2 525 99099 z 4 -1 155232 z 3 70560 z 2 -1 8960 z 128 PolyLog 2 -1 z 1 2 2097152 z 1 2 -1 -1 525 99099 z 4 -1 155232 z 3 70560 z 2 -1 8960 z 128 PolyLog 2 z 1 2 2097152 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02