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 HypergeometricPFQ

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

 Input Form

 HypergeometricPFQ[{1/2, 1, 1}, {7/2, 7/2}, -z] == (25 (72 Pi^2 - 888 Sqrt[z] - 216 Pi^2 z + 1388 z^(3/2) + 27 Pi^2 z^2))/ (768 z^(5/2)) + (25 (54 - 36 z - 262 z^2 - 253 z^3 + 9 z^4) Log[1 + Sqrt[z] - Sqrt[1 + z]])/(144 z^2 (1 + z)^(5/2)) - (25 (54 - 36 z - 262 z^2 - 253 z^3 + 9 z^4) Log[1 - Sqrt[z] + Sqrt[1 + z]])/ (144 z^2 (1 + z)^(5/2)) - (125 Sqrt[1 + z] (-10 + 11 z) Log[Sqrt[z] + Sqrt[1 + z]])/(64 z^(5/2)) - (25 (54 - 36 z - 262 z^2 - 253 z^3 + 9 z^4) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (144 z^2 (1 + z)^(5/2)) + (75 (8 - 24 z + 3 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (64 z^(5/2)) + (75 (8 - 24 z + 3 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(64 z^(5/2)) - (75 (8 - 24 z + 3 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/(64 z^(5/2))

 Standard Form

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 MathML Form

 3 F 2 ( 1 2 , 1 , 1 ; 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["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["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[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] 25 ( 27 π 2 z 2 + 1388 z 3 / 2 - 216 π 2 z - 888 z + 72 π 2 ) 768 z 5 / 2 + 25 ( 9 z 4 - 253 z 3 - 262 z 2 - 36 z + 54 ) log ( z - z + 1 + 1 ) 144 z 2 ( z + 1 ) 5 / 2 - 25 ( 9 z 4 - 253 z 3 - 262 z 2 - 36 z + 54 ) log ( - z + z + 1 + 1 ) 144 z 2 ( z + 1 ) 5 / 2 - 125 z + 1 ( 11 z - 10 ) log ( z + z + 1 ) 64 z 5 / 2 - 25 ( 9 z 4 - 253 z 3 - 262 z 2 - 36 z + 54 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 144 z 2 ( z + 1 ) 5 / 2 + 75 ( 3 z 2 - 24 z + 8 ) log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) 64 z 5 / 2 + 75 ( 3 z 2 - 24 z + 8 ) Li PolyLog 2 ( - 1 z + z + 1 ) 64 z 5 / 2 - 75 ( 3 z 2 - 24 z + 8 ) Li PolyLog 2 ( 1 z + z + 1 ) 64 z 5 / 2 HypergeometricPFQ 1 2 1 1 7 2 7 2 -1 z 25 27 2 z 2 1388 z 3 2 -1 216 2 z -1 888 z 1 2 72 2 768 z 5 2 -1 25 9 z 4 -1 253 z 3 -1 262 z 2 -1 36 z 54 z 1 2 -1 z 1 1 2 1 144 z 2 z 1 5 2 -1 -1 25 9 z 4 -1 253 z 3 -1 262 z 2 -1 36 z 54 -1 z 1 2 z 1 1 2 1 144 z 2 z 1 5 2 -1 -1 125 z 1 1 2 11 z -10 z 1 2 z 1 1 2 64 z 5 2 -1 -1 25 9 z 4 -1 253 z 3 -1 262 z 2 -1 36 z 54 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 144 z 2 z 1 5 2 -1 75 3 z 2 -1 24 z 8 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 64 z 5 2 -1 75 3 z 2 -1 24 z 8 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 64 z 5 2 -1 -1 75 3 z 2 -1 24 z 8 PolyLog 2 1 z 1 2 z 1 1 2 -1 64 z 5 2 -1 [/itex]

 Rule Form

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

 2007-05-02