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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9226.01

 Input Form

 HypergeometricPFQ[{-(7/2), 3, 3}, {-(3/2), -(3/2)}, z] == (1/(1024 (-1 + z)^5)) (-1024 + 19456 z - 1228800 z^2 + 1389150 I Pi^2 z^(5/2) + 43554580 z^3 - 18951975 I Pi^2 z^(7/2) - 216934420 z^4 + 73922625 I Pi^2 z^(9/2) + 445988664 z^5 - 133953750 I Pi^2 z^(11/2) - 458558856 z^6 + 127008000 I Pi^2 z^(13/2) + 235008900 z^7 - 61420275 I Pi^2 z^(15/2) - 48024900 z^8 + 12006225 I Pi^2 z^(17/2)) - (1/(256 (-1 + z)^6)) (315 Sqrt[1 - z] (11207 z^(5/2) - 103914 z^(7/2) + 335585 z^(9/2) - 536556 z^(11/2) + 463113 z^(13/2) - 207690 z^(15/2) + 38115 z^(17/2)) ArcSin[Sqrt[z]]) + (1/(3145728 (-1 + z)^13)) (Sqrt[1 - z] (3145728 - 104166912 z + 6842745600 z^2 - 418172148800 z^3 + 4963013624800 z^4 - 33407797375736 z^5 + 128290598240644 z^6 - 343341200456000 z^7 + 655492887066475 z^8 - 922973276734325 z^9 + 970385037278713 z^10 - 762186592321427 z^11 + 441930830607000 z^12 - 183938855221800 z^13 + 52061039906400 z^14 - 8983760345280 z^15 + 714021073920 z^16) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(3145728 (-1 + z)^13)) (Sqrt[1 - z] (-3145728 + 104166912 z - 6842745600 z^2 + 418172148800 z^3 - 4963013624800 z^4 + 33407797375736 z^5 - 128290598240644 z^6 + 343341200456000 z^7 - 655492887066475 z^8 + 922973276734325 z^9 - 970385037278713 z^10 + 762186592321427 z^11 - 441930830607000 z^12 + 183938855221800 z^13 - 52061039906400 z^14 + 8983760345280 z^15 - 714021073920 z^16) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) + (99225/256) (-14 z^(5/2) + 121 z^(7/2)) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))] - (1/(3145728 (-1 + z)^13)) (Sqrt[1 - z] (3145728 - 104166912 z + 6842745600 z^2 - 418172148800 z^3 + 4963013624800 z^4 - 33407797375736 z^5 + 128290598240644 z^6 - 343341200456000 z^7 + 655492887066475 z^8 - 922973276734325 z^9 + 970385037278713 z^10 - 762186592321427 z^11 + 441930830607000 z^12 - 183938855221800 z^13 + 52061039906400 z^14 - 8983760345280 z^15 + 714021073920 z^16) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (99225/256) I (-14 z^(5/2) + 121 z^(7/2)) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] - (99225/256) I (-14 z^(5/2) + 121 z^(7/2)) PolyLog[2, E^(I ArcSin[Sqrt[z]])]

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 3 , 3 ; - 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["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["3", "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["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 1024 ( z - 1 ) 5 ( 12006225 π 2 z 17 / 2 - 48024900 z 8 - 61420275 π 2 z 15 / 2 + 235008900 z 7 + 127008000 π 2 z 13 / 2 - 458558856 z 6 - 133953750 π 2 z 11 / 2 + 445988664 z 5 + 73922625 π 2 z 9 / 2 - 216934420 z 4 - 18951975 π 2 z 7 / 2 + 43554580 z 3 + 1389150 π 2 z 5 / 2 - 1228800 z 2 + 19456 z - 1024 ) - 1 256 ( z - 1 ) 6 ( 315 1 - z ( 38115 z 17 / 2 - 207690 z 15 / 2 + 463113 z 13 / 2 - 536556 z 11 / 2 + 335585 z 9 / 2 - 103914 z 7 / 2 + 11207 z 5 / 2 ) sin - 1 ( z ) ) + 1 3145728 ( z - 1 ) 13 ( 1 - z ( 714021073920 z 16 - 8983760345280 z 15 + 52061039906400 z 14 - 183938855221800 z 13 + 441930830607000 z 12 - 762186592321427 z 11 + 970385037278713 z 10 - 922973276734325 z 9 + 655492887066475 z 8 - 343341200456000 z 7 + 128290598240644 z 6 - 33407797375736 z 5 + 4963013624800 z 4 - 418172148800 z 3 + 6842745600 z 2 - 104166912 z + 3145728 ) log ( 1 - sin - 1 ( z ) ) ) + 1 3145728 ( z - 1 ) 13 ( 1 - z ( - 714021073920 z 16 + 8983760345280 z 15 - 52061039906400 z 14 + 183938855221800 z 13 - 441930830607000 z 12 + 762186592321427 z 11 - 970385037278713 z 10 + 922973276734325 z 9 - 655492887066475 z 8 + 343341200456000 z 7 - 128290598240644 z 6 + 33407797375736 z 5 - 4963013624800 z 4 + 418172148800 z 3 - 6842745600 z 2 + 104166912 z - 3145728 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) ) + 99225 256 ( 121 z 7 / 2 - 14 z 5 / 2 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) - 1 3145728 ( z - 1 ) 13 ( 1 - z ( 714021073920 z 16 - 8983760345280 z 15 + 52061039906400 z 14 - 183938855221800 z 13 + 441930830607000 z 12 - 762186592321427 z 11 + 970385037278713 z 10 - 922973276734325 z 9 + 655492887066475 z 8 - 343341200456000 z 7 + 128290598240644 z 6 - 33407797375736 z 5 + 4963013624800 z 4 - 418172148800 z 3 + 6842745600 z 2 - 104166912 z + 3145728 ) log ( 1 + sin - 1 ( z ) ) ) + 99225 256 ( 121 z 7 / 2 - 14 z 5 / 2 ) Li PolyLog 2 ( - sin - 1 ( z ) ) - 99225 256 ( 121 z 7 / 2 - 14 z 5 / 2 ) Li PolyLog 2 ( sin - 1 ( z ) ) HypergeometricPFQ -1 7 2 3 3 -1 3 2 -1 3 2 z 1 1024 z -1 5 -1 12006225 2 z 17 2 -1 48024900 z 8 -1 61420275 2 z 15 2 235008900 z 7 127008000 2 z 13 2 -1 458558856 z 6 -1 133953750 2 z 11 2 445988664 z 5 73922625 2 z 9 2 -1 216934420 z 4 -1 18951975 2 z 7 2 43554580 z 3 1389150 2 z 5 2 -1 1228800 z 2 19456 z -1024 -1 1 256 z -1 6 -1 315 1 -1 z 1 2 38115 z 17 2 -1 207690 z 15 2 463113 z 13 2 -1 536556 z 11 2 335585 z 9 2 -1 103914 z 7 2 11207 z 5 2 z 1 2 1 3145728 z -1 13 -1 1 -1 z 1 2 714021073920 z 16 -1 8983760345280 z 15 52061039906400 z 14 -1 183938855221800 z 13 441930830607000 z 12 -1 762186592321427 z 11 970385037278713 z 10 -1 922973276734325 z 9 655492887066475 z 8 -1 343341200456000 z 7 128290598240644 z 6 -1 33407797375736 z 5 4963013624800 z 4 -1 418172148800 z 3 6842745600 z 2 -1 104166912 z 3145728 1 -1 z 1 2 1 3145728 z -1 13 -1 1 -1 z 1 2 -714021073920 z 16 8983760345280 z 15 -1 52061039906400 z 14 183938855221800 z 13 -1 441930830607000 z 12 762186592321427 z 11 -1 970385037278713 z 10 922973276734325 z 9 -1 655492887066475 z 8 343341200456000 z 7 -1 128290598240644 z 6 33407797375736 z 5 -1 4963013624800 z 4 418172148800 z 3 -1 6842745600 z 2 104166912 z -3145728 1 -1 z 1 2 1 z 1 2 -1 99225 256 121 z 7 2 -1 14 z 5 2 z 1 2 1 -1 z 1 2 1 z 1 2 -1 -1 1 3145728 z -1 13 -1 1 -1 z 1 2 714021073920 z 16 -1 8983760345280 z 15 52061039906400 z 14 -1 183938855221800 z 13 441930830607000 z 12 -1 762186592321427 z 11 970385037278713 z 10 -1 922973276734325 z 9 655492887066475 z 8 -1 343341200456000 z 7 128290598240644 z 6 -1 33407797375736 z 5 4963013624800 z 4 -1 418172148800 z 3 6842745600 z 2 -1 104166912 z 3145728 1 z 1 2 99225 256 121 z 7 2 -1 14 z 5 2 PolyLog 2 -1 z 1 2 -1 99225 256 121 z 7 2 -1 14 z 5 2 PolyLog 2 z 1 2 [/itex]

 Rule Form

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

 2007-05-02