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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9230.01

 Input Form

 HypergeometricPFQ[{-(7/2), 3, 3}, {-(3/2), 1/2}, z] == (1/(8192 (-1 + z)^3)) (-8192 - 277488 z - 7257424 z^2 + 4167450 I Pi^2 z^(5/2) + 68914260 z^3 - 24508575 I Pi^2 z^(7/2) - 163485756 z^4 + 48521025 I Pi^2 z^(9/2) + 150072300 z^5 - 40186125 I Pi^2 z^(11/2) - 48024900 z^6 + 12006225 I Pi^2 z^(13/2)) - (1/(2048 (-1 + z)^4)) (105 Sqrt[1 - z] (-100 Sqrt[z] - 2100 z^(3/2) + 79233 z^(5/2) - 345132 z^(7/2) + 574434 z^(9/2) - 420840 z^(11/2) + 114345 z^(13/2)) ArcSin[Sqrt[z]]) + (1/(3145728 (-1 + z)^11)) (Sqrt[1 - z] (3145728 + 161505792 z + 3920345856 z^2 - 116747471680 z^3 + 964517263584 z^4 - 4402368255768 z^5 + 12682072978148 z^6 - 24991291866336 z^7 + 34931376770955 z^8 - 35137741608529 z^9 + 25359434581005 z^10 - 12846309221655 z^11 + 4345500513060 z^12 - 882827051400 z^13 + 81568650240 z^14) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(3145728 (-1 + z)^11)) (Sqrt[1 - z] (-3145728 - 161505792 z - 3920345856 z^2 + 116747471680 z^3 - 964517263584 z^4 + 4402368255768 z^5 - 12682072978148 z^6 + 24991291866336 z^7 - 34931376770955 z^8 + 35137741608529 z^9 - 25359434581005 z^10 + 12846309221655 z^11 - 4345500513060 z^12 + 882827051400 z^13 - 81568650240 z^14) Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))]) + (99225 (-42 z^(5/2) + 121 z^(7/2)) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/2048 - (1/(3145728 (-1 + z)^11)) (Sqrt[1 - z] (3145728 + 161505792 z + 3920345856 z^2 - 116747471680 z^3 + 964517263584 z^4 - 4402368255768 z^5 + 12682072978148 z^6 - 24991291866336 z^7 + 34931376770955 z^8 - 35137741608529 z^9 + 25359434581005 z^10 - 12846309221655 z^11 + 4345500513060 z^12 - 882827051400 z^13 + 81568650240 z^14) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (99225 I (-42 z^(5/2) + 121 z^(7/2)) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ 2048 - (99225 I (-42 z^(5/2) + 121 z^(7/2)) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/2048

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 3 , 3 ; - 3 2 , 1 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[FractionBox["1", "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 8192 ( z - 1 ) 3 ( 12006225 π 2 z 13 / 2 - 48024900 z 6 - 40186125 π 2 z 11 / 2 + 150072300 z 5 + 48521025 π 2 z 9 / 2 - 163485756 z 4 - 24508575 π 2 z 7 / 2 + 68914260 z 3 + 4167450 π 2 z 5 / 2 - 7257424 z 2 - 277488 z - 8192 ) - 1 2048 ( z - 1 ) 4 ( 105 1 - z ( 114345 z 13 / 2 - 420840 z 11 / 2 + 574434 z 9 / 2 - 345132 z 7 / 2 + 79233 z 5 / 2 - 2100 z 3 / 2 - 100 z ) sin - 1 ( z ) ) + 1 3145728 ( z - 1 ) 11 ( 1 - z ( 81568650240 z 14 - 882827051400 z 13 + 4345500513060 z 12 - 12846309221655 z 11 + 25359434581005 z 10 - 35137741608529 z 9 + 34931376770955 z 8 - 24991291866336 z 7 + 12682072978148 z 6 - 4402368255768 z 5 + 964517263584 z 4 - 116747471680 z 3 + 3920345856 z 2 + 161505792 z + 3145728 ) log ( 1 - sin - 1 ( z ) ) ) + 1 3145728 ( z - 1 ) 11 ( 1 - z ( - 81568650240 z 14 + 882827051400 z 13 - 4345500513060 z 12 + 12846309221655 z 11 - 25359434581005 z 10 + 35137741608529 z 9 - 34931376770955 z 8 + 24991291866336 z 7 - 12682072978148 z 6 + 4402368255768 z 5 - 964517263584 z 4 + 116747471680 z 3 - 3920345856 z 2 - 161505792 z - 3145728 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) ) + 99225 ( 121 z 7 / 2 - 42 z 5 / 2 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 2048 - 1 3145728 ( z - 1 ) 11 ( 1 - z ( 81568650240 z 14 - 882827051400 z 13 + 4345500513060 z 12 - 12846309221655 z 11 + 25359434581005 z 10 - 35137741608529 z 9 + 34931376770955 z 8 - 24991291866336 z 7 + 12682072978148 z 6 - 4402368255768 z 5 + 964517263584 z 4 - 116747471680 z 3 + 3920345856 z 2 + 161505792 z + 3145728 ) log ( 1 + sin - 1 ( z ) ) ) + 99225 ( 121 z 7 / 2 - 42 z 5 / 2 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 2048 - 99225 ( 121 z 7 / 2 - 42 z 5 / 2 ) Li PolyLog 2 ( sin - 1 ( z ) ) 2048 HypergeometricPFQ -1 7 2 3 3 -1 3 2 1 2 z 1 8192 z -1 3 -1 12006225 2 z 13 2 -1 48024900 z 6 -1 40186125 2 z 11 2 150072300 z 5 48521025 2 z 9 2 -1 163485756 z 4 -1 24508575 2 z 7 2 68914260 z 3 4167450 2 z 5 2 -1 7257424 z 2 -1 277488 z -8192 -1 1 2048 z -1 4 -1 105 1 -1 z 1 2 114345 z 13 2 -1 420840 z 11 2 574434 z 9 2 -1 345132 z 7 2 79233 z 5 2 -1 2100 z 3 2 -1 100 z 1 2 z 1 2 1 3145728 z -1 11 -1 1 -1 z 1 2 81568650240 z 14 -1 882827051400 z 13 4345500513060 z 12 -1 12846309221655 z 11 25359434581005 z 10 -1 35137741608529 z 9 34931376770955 z 8 -1 24991291866336 z 7 12682072978148 z 6 -1 4402368255768 z 5 964517263584 z 4 -1 116747471680 z 3 3920345856 z 2 161505792 z 3145728 1 -1 z 1 2 1 3145728 z -1 11 -1 1 -1 z 1 2 -81568650240 z 14 882827051400 z 13 -1 4345500513060 z 12 12846309221655 z 11 -1 25359434581005 z 10 35137741608529 z 9 -1 34931376770955 z 8 24991291866336 z 7 -1 12682072978148 z 6 4402368255768 z 5 -1 964517263584 z 4 116747471680 z 3 -1 3920345856 z 2 -1 161505792 z -3145728 1 -1 z 1 2 1 z 1 2 -1 99225 121 z 7 2 -1 42 z 5 2 z 1 2 1 -1 z 1 2 1 z 1 2 -1 2048 -1 -1 1 3145728 z -1 11 -1 1 -1 z 1 2 81568650240 z 14 -1 882827051400 z 13 4345500513060 z 12 -1 12846309221655 z 11 25359434581005 z 10 -1 35137741608529 z 9 34931376770955 z 8 -1 24991291866336 z 7 12682072978148 z 6 -1 4402368255768 z 5 964517263584 z 4 -1 116747471680 z 3 3920345856 z 2 161505792 z 3145728 1 z 1 2 99225 121 z 7 2 -1 42 z 5 2 PolyLog 2 -1 z 1 2 2048 -1 -1 99225 121 z 7 2 -1 42 z 5 2 PolyLog 2 z 1 2 2048 -1 [/itex]

 Rule Form

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

 2007-05-02