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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.as31.01

 Input Form

 HypergeometricPFQ[{3/2, 2, 4}, {7/2, 7/2}, z] == -((75 I (-6 Pi^2 - 52 I Sqrt[z] + 3 Pi^2 z))/(512 z^(5/2))) + (75 Sqrt[1 - z] (-7 + 3 z) ArcSin[Sqrt[z]])/(128 (-1 + z) z^(5/2)) + (25 Sqrt[1 - z] (18 - 69 z + 122 z^2 - 82 z^3 + 21 z^4) Log[1 - E^(I ArcSin[Sqrt[z]])])/(128 (-1 + z)^4 z^2) - (25 Sqrt[1 - z] (18 - 69 z + 122 z^2 - 82 z^3 + 21 z^4) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (128 (-1 + z)^4 z^2) - (225 (-2 + z) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (128 z^(5/2)) - (25 Sqrt[1 - z] (18 - 69 z + 122 z^2 - 82 z^3 + 21 z^4) Log[1 + E^(I ArcSin[Sqrt[z]])])/(128 (-1 + z)^4 z^2) - (225 I (-2 + z) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(128 z^(5/2)) + (225 I (-2 + z) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(128 z^(5/2))

 Standard Form

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 MathML Form

 3 F 2 ( 3 2 , 2 , 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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", 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] - 75 ( 3 π 2 z - 52 z - 6 π 2 ) 512 z 5 / 2 + 75 1 - z ( 3 z - 7 ) sin - 1 ( z ) 128 ( z - 1 ) z 5 / 2 + 25 1 - z ( 21 z 4 - 82 z 3 + 122 z 2 - 69 z + 18 ) log ( 1 - sin - 1 ( z ) ) 128 ( z - 1 ) 4 z 2 - 25 1 - z ( 21 z 4 - 82 z 3 + 122 z 2 - 69 z + 18 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 128 ( z - 1 ) 4 z 2 - 225 ( z - 2 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 128 z 5 / 2 - 25 1 - z ( 21 z 4 - 82 z 3 + 122 z 2 - 69 z + 18 ) log ( 1 + sin - 1 ( z ) ) 128 ( z - 1 ) 4 z 2 - 225 ( z - 2 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 128 z 5 / 2 + 225 ( z - 2 ) Li PolyLog 2 ( sin - 1 ( z ) ) 128 z 5 / 2 HypergeometricPFQ 3 2 2 4 7 2 7 2 z -1 75 3 2 z -1 52 z 1 2 -1 6 2 512 z 5 2 -1 75 1 -1 z 1 2 3 z -7 z 1 2 128 z -1 z 5 2 -1 25 1 -1 z 1 2 21 z 4 -1 82 z 3 122 z 2 -1 69 z 18 1 -1 z 1 2 128 z -1 4 z 2 -1 -1 25 1 -1 z 1 2 21 z 4 -1 82 z 3 122 z 2 -1 69 z 18 1 -1 z 1 2 1 z 1 2 -1 128 z -1 4 z 2 -1 -1 225 z -2 z 1 2 1 -1 z 1 2 1 z 1 2 -1 128 z 5 2 -1 -1 25 1 -1 z 1 2 21 z 4 -1 82 z 3 122 z 2 -1 69 z 18 1 z 1 2 128 z -1 4 z 2 -1 -1 225 z -2 PolyLog 2 -1 z 1 2 128 z 5 2 -1 225 z -2 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