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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.a7va.01

 Input Form

 HypergeometricPFQ[{-(5/2), -(5/2), -(1/2)}, {3/2, 7/2}, z] == (125 (Pi^2 - 6 Pi^2 z))/(16384 Sqrt[-z]) + (Sqrt[1 - z] (45 - 2220 z + 1199388 z^2 - 310976 z^3 - 11872 z^4))/ (1572864 z^2) + (5 (-3 + 150 z + 15200 z^2 + 52800 z^3 - 9600 z^4 - 256 z^5) Log[Sqrt[1 - z] + Sqrt[-z]])/(524288 (-z)^(5/2)) - (375 (1 - 6 z) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(8192 Sqrt[-z]) + (375 (1 - 6 z) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (4096 Sqrt[-z]) + (375 (1 - 6 z) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ (4096 Sqrt[-z]) - (375 (1 - 6 z) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (4096 Sqrt[-z])

 Standard Form

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 MathML Form

 3 F 2 ( - 5 2 , - 5 2 , - 1 2 ; 3 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[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "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["3", "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] - 375 ( 1 - 6 z ) log 2 ( 1 - z + - z ) 8192 - z + 5 ( - 256 z 5 - 9600 z 4 + 52800 z 3 + 15200 z 2 + 150 z - 3 ) log ( 1 - z + - z ) 524288 ( - z ) 5 / 2 + 375 ( 1 - 6 z ) log ( 1 - z + - z + 1 ) log ( 1 - z + - z ) 4096 - z + 125 ( π 2 - 6 π 2 z ) 16384 - z + 1 - z ( - 11872 z 4 - 310976 z 3 + 1199388 z 2 - 2220 z + 45 ) 1572864 z 2 + 375 ( 1 - 6 z ) Li PolyLog 2 ( - 1 - z - - z ) 4096 - z - 375 ( 1 - 6 z ) Li PolyLog 2 ( - 1 - z - - z + 1 ) 4096 - z HypergeometricPFQ -1 5 2 -1 5 2 -1 1 2 3 2 7 2 z -1 375 1 -1 6 z 1 -1 z 1 2 -1 z 1 2 2 8192 -1 z 1 2 -1 5 -256 z 5 -1 9600 z 4 52800 z 3 15200 z 2 150 z -3 1 -1 z 1 2 -1 z 1 2 524288 -1 z 5 2 -1 375 1 -1 6 z 1 -1 z 1 2 -1 z 1 2 1 1 -1 z 1 2 -1 z 1 2 4096 -1 z 1 2 -1 125 2 -1 6 2 z 16384 -1 z 1 2 -1 1 -1 z 1 2 -11872 z 4 -1 310976 z 3 1199388 z 2 -1 2220 z 45 1572864 z 2 -1 375 1 -1 6 z PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 4096 -1 z 1 2 -1 -1 375 1 -1 6 z PolyLog 2 -1 1 -1 z 1 2 -1 -1 z 1 2 1 4096 -1 z 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02