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 HypergeometricPFQ

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

 Input Form

 HypergeometricPFQ[{1/2, 1, 3}, {5/2, 5/2}, -z] == (9 (2 Pi^2 - 20 Sqrt[z] + 3 Pi^2 z))/(128 z^(3/2)) + ((18 + 85 z + 97 z^2 + 36 z^3) Log[1 + Sqrt[z] - Sqrt[1 + z]])/ (32 z (1 + z)^(5/2)) + ((-18 - 85 z - 97 z^2 - 36 z^3) Log[1 - Sqrt[z] + Sqrt[1 + z]])/(32 z (1 + z)^(5/2)) + (27 Sqrt[1 + z] Log[Sqrt[z] + Sqrt[1 + z]])/(32 z^(3/2)) + ((-18 - 85 z - 97 z^2 - 36 z^3) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])])/(32 z (1 + z)^(5/2)) + (9 (2 + 3 z) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (32 z^(3/2)) + (9 (2 + 3 z) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/ (32 z^(3/2)) - (9 (2 + 3 z) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (32 z^(3/2))

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 3 ; 5 2 , 5 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["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 9 ( 3 π 2 z - 20 z + 2 π 2 ) 128 z 3 / 2 + ( 36 z 3 + 97 z 2 + 85 z + 18 ) log ( z - z + 1 + 1 ) 32 z ( z + 1 ) 5 / 2 + ( - 36 z 3 - 97 z 2 - 85 z - 18 ) log ( - z + z + 1 + 1 ) 32 z ( z + 1 ) 5 / 2 + 27 z + 1 log ( z + z + 1 ) 32 z 3 / 2 + ( - 36 z 3 - 97 z 2 - 85 z - 18 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 32 z ( z + 1 ) 5 / 2 + 9 ( 3 z + 2 ) log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 32 z 3 / 2 + 9 ( 3 z + 2 ) Li PolyLog 2 ( - 1 z + z + 1 ) 32 z 3 / 2 - 9 ( 3 z + 2 ) Li PolyLog 2 ( 1 z + z + 1 ) 32 z 3 / 2 HypergeometricPFQ 1 2 1 3 5 2 5 2 -1 z 9 3 2 z -1 20 z 1 2 2 2 128 z 3 2 -1 36 z 3 97 z 2 85 z 18 z 1 2 -1 z 1 1 2 1 32 z z 1 5 2 -1 -36 z 3 -1 97 z 2 -1 85 z -18 -1 z 1 2 z 1 1 2 1 32 z z 1 5 2 -1 27 z 1 1 2 z 1 2 z 1 1 2 32 z 3 2 -1 -36 z 3 -1 97 z 2 -1 85 z -18 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 32 z z 1 5 2 -1 9 3 z 2 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 32 z 3 2 -1 9 3 z 2 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 32 z 3 2 -1 -1 9 3 z 2 PolyLog 2 1 z 1 2 z 1 1 2 -1 32 z 3 2 -1 [/itex]

 Rule Form

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

 2007-05-02