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 HypergeometricPFQ

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

 Input Form

 HypergeometricPFQ[{1/2, 1, 1}, {5/2, 7/2}, -z] == (5 (-24 - 36 Pi^2 Sqrt[z] + 292 z + 9 Pi^2 z^(3/2)))/(64 z^2) + (5 (-18 - 23 z + z^2) Log[1 + Sqrt[z] - Sqrt[1 + z]])/(8 z (1 + z)^(3/2)) - (5 (-18 - 23 z + z^2) Log[1 - Sqrt[z] + Sqrt[1 + z]])/(8 z (1 + z)^(3/2)) - (15 Sqrt[1 + z] (-2 + 13 z) Log[Sqrt[z] + Sqrt[1 + z]])/(16 z^(5/2)) - (5 (-18 - 23 z + z^2) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])])/(8 z (1 + z)^(3/2)) + (45 (-4 + z) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (16 z^(3/2)) + (45 (-4 + z) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/ (16 z^(3/2)) - (45 (-4 + z) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (16 z^(3/2))

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 1 ; 5 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["1", 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["7", "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] 5 ( 9 π 2 z 3 / 2 + 292 z - 36 π 2 z - 24 ) 64 z 2 + 5 ( z 2 - 23 z - 18 ) log ( z - z + 1 + 1 ) 8 z ( z + 1 ) 3 / 2 - 5 ( z 2 - 23 z - 18 ) log ( - z + z + 1 + 1 ) 8 z ( z + 1 ) 3 / 2 - 15 z + 1 ( 13 z - 2 ) log ( z + z + 1 ) 16 z 5 / 2 - 5 ( z 2 - 23 z - 18 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 8 z ( z + 1 ) 3 / 2 + 45 ( z - 4 ) log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 16 z 3 / 2 + 45 ( z - 4 ) Li PolyLog 2 ( - 1 z + z + 1 ) 16 z 3 / 2 - 45 ( z - 4 ) Li PolyLog 2 ( 1 z + z + 1 ) 16 z 3 / 2 HypergeometricPFQ 1 2 1 1 5 2 7 2 -1 z 5 9 2 z 3 2 292 z -1 36 2 z 1 2 -24 64 z 2 -1 5 z 2 -1 23 z -18 z 1 2 -1 z 1 1 2 1 8 z z 1 3 2 -1 -1 5 z 2 -1 23 z -18 -1 z 1 2 z 1 1 2 1 8 z z 1 3 2 -1 -1 15 z 1 1 2 13 z -2 z 1 2 z 1 1 2 16 z 5 2 -1 -1 5 z 2 -1 23 z -18 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 8 z z 1 3 2 -1 45 z -4 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 16 z 3 2 -1 45 z -4 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 16 z 3 2 -1 -1 45 z -4 PolyLog 2 1 z 1 2 z 1 1 2 -1 16 z 3 2 -1 [/itex]

 Rule Form

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

 2007-05-02