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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.an4h.01

 Input Form

 HypergeometricPFQ[{1/2, 1, 2}, {5/2, 7/2}, z] == (15 I (-24 I - 12 Pi^2 Sqrt[z] - 52 I z + 3 Pi^2 z^(3/2)))/(128 z^2) - (45 Sqrt[1 - z] (2 + z) ArcSin[Sqrt[z]])/(32 z^(5/2)) - (15 Sqrt[1 - z] (-12 + 7 z - 40 z^2 + 9 z^3) Log[1 - E^(I ArcSin[Sqrt[z]])])/(32 (-1 + z)^3 z) + (15 Sqrt[1 - z] (-12 + 7 z - 40 z^2 + 9 z^3) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (32 (-1 + z)^3 z) + (45 (-4 + z) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (32 z^(3/2)) + (15 Sqrt[1 - z] (-12 + 7 z - 40 z^2 + 9 z^3) Log[1 + E^(I ArcSin[Sqrt[z]])])/(32 (-1 + z)^3 z) + (45 I (-4 + z) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(32 z^(3/2)) - (45 I (-4 + z) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(32 z^(3/2))

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 2 ; 5 2 , 7 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", 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["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "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] 15 ( 3 π 2 z 3 / 2 - 52 z - 12 π 2 z - 24 ) 128 z 2 - 45 1 - z ( z + 2 ) sin - 1 ( z ) 32 z 5 / 2 - 15 1 - z ( 9 z 3 - 40 z 2 + 7 z - 12 ) log ( 1 - sin - 1 ( z ) ) 32 ( z - 1 ) 3 z + 15 1 - z ( 9 z 3 - 40 z 2 + 7 z - 12 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 32 ( z - 1 ) 3 z + 45 ( z - 4 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 32 z 3 / 2 + 15 1 - z ( 9 z 3 - 40 z 2 + 7 z - 12 ) log ( 1 + sin - 1 ( z ) ) 32 ( z - 1 ) 3 z + 45 ( z - 4 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 32 z 3 / 2 - 45 ( z - 4 ) Li PolyLog 2 ( sin - 1 ( z ) ) 32 z 3 / 2 HypergeometricPFQ 1 2 1 2 5 2 7 2 z 15 3 2 z 3 2 -1 52 z -1 12 2 z 1 2 -1 24 128 z 2 -1 -1 45 1 -1 z 1 2 z 2 z 1 2 32 z 5 2 -1 -1 15 1 -1 z 1 2 9 z 3 -1 40 z 2 7 z -12 1 -1 z 1 2 32 z -1 3 z -1 15 1 -1 z 1 2 9 z 3 -1 40 z 2 7 z -12 1 -1 z 1 2 1 z 1 2 -1 32 z -1 3 z -1 45 z -4 z 1 2 1 -1 z 1 2 1 z 1 2 -1 32 z 3 2 -1 15 1 -1 z 1 2 9 z 3 -1 40 z 2 7 z -12 1 z 1 2 32 z -1 3 z -1 45 z -4 PolyLog 2 -1 z 1 2 32 z 3 2 -1 -1 45 z -4 PolyLog 2 z 1 2 32 z 3 2 -1 [/itex]

 Rule Form

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

 2007-05-02