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 HypergeometricPFQ

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

 Input Form

 HypergeometricPFQ[{1/2, 1, 3}, {7/2, 7/2}, z] == (25 I (72 Pi^2 + 504 I Sqrt[z] - 72 Pi^2 z - 404 I z^(3/2) + 27 Pi^2 z^2))/ (2048 z^(5/2)) - (675 Sqrt[1 - z] (-2 + z) ArcSin[Sqrt[z]])/ (512 z^(5/2)) - (1/(512 (-1 + z)^5 z^2)) (25 Sqrt[1 - z] (72 - 384 z + 2235 z^2 - 1269 z^3 + 1101 z^4 - 427 z^5 + 72 z^6) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(512 (-1 + z)^5 z^2)) (25 Sqrt[1 - z] (72 - 384 z + 2235 z^2 - 1269 z^3 + 1101 z^4 - 427 z^5 + 72 z^6) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) + (225 (8 - 8 z + 3 z^2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (512 z^(5/2)) + (1/(512 (-1 + z)^5 z^2)) (25 Sqrt[1 - z] (72 - 384 z + 2235 z^2 - 1269 z^3 + 1101 z^4 - 427 z^5 + 72 z^6) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (225 I (8 - 8 z + 3 z^2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (512 z^(5/2)) - (225 I (8 - 8 z + 3 z^2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(512 z^(5/2))

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 3 ; 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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", 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[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 ( 27 π 2 z 2 - 404 z 3 / 2 - 72 π 2 z + 504 z + 72 π 2 ) 2048 z 5 / 2 - 675 1 - z ( z - 2 ) sin - 1 ( z ) 512 z 5 / 2 - 25 1 - z ( 72 z 6 - 427 z 5 + 1101 z 4 - 1269 z 3 + 2235 z 2 - 384 z + 72 ) log ( 1 - sin - 1 ( z ) ) 512 ( z - 1 ) 5 z 2 + 25 1 - z ( 72 z 6 - 427 z 5 + 1101 z 4 - 1269 z 3 + 2235 z 2 - 384 z + 72 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 512 ( z - 1 ) 5 z 2 + 225 ( 3 z 2 - 8 z + 8 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 512 z 5 / 2 + 25 1 - z ( 72 z 6 - 427 z 5 + 1101 z 4 - 1269 z 3 + 2235 z 2 - 384 z + 72 ) log ( 1 + sin - 1 ( z ) ) 512 ( z - 1 ) 5 z 2 + 225 ( 3 z 2 - 8 z + 8 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 512 z 5 / 2 - 225 ( 3 z 2 - 8 z + 8 ) Li PolyLog 2 ( sin - 1 ( z ) ) 512 z 5 / 2 HypergeometricPFQ 1 2 1 3 7 2 7 2 z 25 27 2 z 2 -1 404 z 3 2 -1 72 2 z 504 z 1 2 72 2 2048 z 5 2 -1 -1 675 1 -1 z 1 2 z -2 z 1 2 512 z 5 2 -1 -1 25 1 -1 z 1 2 72 z 6 -1 427 z 5 1101 z 4 -1 1269 z 3 2235 z 2 -1 384 z 72 1 -1 z 1 2 512 z -1 5 z 2 -1 25 1 -1 z 1 2 72 z 6 -1 427 z 5 1101 z 4 -1 1269 z 3 2235 z 2 -1 384 z 72 1 -1 z 1 2 1 z 1 2 -1 512 z -1 5 z 2 -1 225 3 z 2 -1 8 z 8 z 1 2 1 -1 z 1 2 1 z 1 2 -1 512 z 5 2 -1 25 1 -1 z 1 2 72 z 6 -1 427 z 5 1101 z 4 -1 1269 z 3 2235 z 2 -1 384 z 72 1 z 1 2 512 z -1 5 z 2 -1 225 3 z 2 -1 8 z 8 PolyLog 2 -1 z 1 2 512 z 5 2 -1 -1 225 3 z 2 -1 8 z 8 PolyLog 2 z 1 2 512 z 5 2 -1 [/itex]

 Rule Form

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

 2007-05-02