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 HypergeometricPFQ

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

 Input Form

 HypergeometricPFQ[{5/2, 3, 4}, {7/2, 7/2}, z] == (25 (3 I Pi^2 - 8 Sqrt[z] - 6 I Pi^2 z + 20 z^(3/2) + 3 I Pi^2 z^2))/ (512 (-1 + z)^2 z^(5/2)) - (25 Sqrt[1 - z] (-1 + z + 3 z^2) ArcSin[Sqrt[z]])/(128 (-1 + z)^3 z^(5/2)) - (25 Sqrt[1 - z] (3 - 7 z + z^2) Log[1 - E^(I ArcSin[Sqrt[z]])])/ (128 (-1 + z)^3 z^2) + (25 Sqrt[1 - z] (3 - 7 z + z^2) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (128 (-1 + z)^3 z^2) + (75 ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/(128 z^(5/2)) + (25 Sqrt[1 - z] (3 - 7 z + z^2) Log[1 + E^(I ArcSin[Sqrt[z]])])/ (128 (-1 + z)^3 z^2) + (75 I PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (128 z^(5/2)) - (75 I PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(128 z^(5/2))

 Standard Form

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 MathML Form

 3 F 2 ( 5 2 , 3 , 4 ; 7 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["5", "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["7", "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] 25 ( 3 π 2 z 2 + 20 z 3 / 2 - 6 π 2 z - 8 z + 3 π 2 ) 512 ( z - 1 ) 2 z 5 / 2 - 25 1 - z ( 3 z 2 + z - 1 ) sin - 1 ( z ) 128 ( z - 1 ) 3 z 5 / 2 - 25 1 - z ( z 2 - 7 z + 3 ) log ( 1 - sin - 1 ( z ) ) 128 ( z - 1 ) 3 z 2 + 25 1 - z ( z 2 - 7 z + 3 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 128 ( z - 1 ) 3 z 2 + 75 sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 128 z 5 / 2 + 25 1 - z ( z 2 - 7 z + 3 ) log ( 1 + sin - 1 ( z ) ) 128 ( z - 1 ) 3 z 2 + 75 Li PolyLog 2 ( - sin - 1 ( z ) ) 128 z 5 / 2 - 75 Li PolyLog 2 ( sin - 1 ( z ) ) 128 z 5 / 2 HypergeometricPFQ 5 2 3 4 7 2 7 2 z 25 3 2 z 2 20 z 3 2 -1 6 2 z -1 8 z 1 2 3 2 512 z -1 2 z 5 2 -1 -1 25 1 -1 z 1 2 3 z 2 z -1 z 1 2 128 z -1 3 z 5 2 -1 -1 25 1 -1 z 1 2 z 2 -1 7 z 3 1 -1 z 1 2 128 z -1 3 z 2 -1 25 1 -1 z 1 2 z 2 -1 7 z 3 1 -1 z 1 2 1 z 1 2 -1 128 z -1 3 z 2 -1 75 z 1 2 1 -1 z 1 2 1 z 1 2 -1 128 z 5 2 -1 25 1 -1 z 1 2 z 2 -1 7 z 3 1 z 1 2 128 z -1 3 z 2 -1 75 PolyLog 2 -1 z 1 2 128 z 5 2 -1 -1 75 PolyLog 2 z 1 2 128 z 5 2 -1 [/itex]

 Rule Form

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

 2007-05-02