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 HypergeometricPFQ

 http://functions.wolfram.com/07.31.03.0021.01

 Input Form

 HypergeometricPFQ[{Subscript[b, 1] - 2, Subscript[b, 2] - 2, \[Ellipsis], Subscript[b, n + 1] - 2, Subscript[b, n + 2] - 1, Subscript[b, n + 3] - 1, \[Ellipsis], Subscript[b, q + 1] - 1}, {Subscript[b, 1], Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z] == (((-1)^n 2^q)/z) ((1/z) Sum[(Pochhammer[n, k]/k!) PolyLog[q - k, z], {k, 0, q - 1}] + Sum[(((-1)^(n - k) Pochhammer[q, k])/k!) PolyLog[n - k, z], {k, 0, n - 1}] - Binomial[n + q - 1, n]) /; Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, q] == 3

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["b", "1"], "-", "2"]], ",", RowBox[List[SubscriptBox["b", "2"], "-", "2"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", RowBox[List["n", "+", "1"]]], "-", "2"]], ",", RowBox[List[SubscriptBox["b", RowBox[List["n", "+", "2"]]], "-", "1"]], ",", RowBox[List[SubscriptBox["b", RowBox[List["n", "+", "3"]]], "-", "1"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", RowBox[List["q", "+", "1"]]], "-", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], SuperscriptBox["2", "q"]]], "z"], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "z"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["q", "-", "1"]]], RowBox[List[FractionBox[RowBox[List["Pochhammer", "[", RowBox[List["n", ",", "k"]], "]"]], RowBox[List["k", "!"]]], RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["q", " ", "-", "k"]], ",", "z"]], "]"]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["n", "-", "1"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "k"]]], RowBox[List["Pochhammer", "[", RowBox[List["q", ",", "k"]], "]"]]]], RowBox[List["k", "!"]]], RowBox[List["PolyLog", "[", RowBox[List[RowBox[List["n", " ", "-", "k"]], ",", "z"]], "]"]]]]]], "-", RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "+", "q", "-", "1"]], ",", "n"]], "]"]]]], ")"]]]]]], "/;", RowBox[List[SubscriptBox["b", "1"], "\[Equal]", SubscriptBox["b", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["b", "q"], "\[Equal]", "3"]]]]]]

 MathML Form

 q + 1 F q ( b 1 - 2 , b 2 - 2 , , b n + 1 - 2 , b n + 2 - 1 , b n + 3 - 1 , , b q + 1 - 1 ; b 1 , b 2 , , b q ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["q", "+", "1"]], TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["b", "1"], "-", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "2"], "-", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", RowBox[List["n", "+", "1"]]], "-", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", RowBox[List["n", "+", "2"]]], "-", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", RowBox[List["n", "+", "3"]]], "-", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", RowBox[List["q", "+", "1"]]], "-", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQRegularized] ( - 1 ) n 2 q z ( 1 z k = 0 q - 1 ( n ) k TagBox[SubscriptBox[RowBox[List["(", "n", ")"]], "k"], Pochhammer] k ! Li PolyLog q - k ( z ) + k = 0 n - 1 ( - 1 ) n - k ( q ) k TagBox[SubscriptBox[RowBox[List["(", "q", ")"]], "k"], Pochhammer] k ! Li PolyLog n - k ( z ) - ( n + q - 1 n ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["n", "+", "q", "-", "1"]], Identity, Rule[Editable, True]]], List[TagBox["n", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ) /; b 1 b 2 b q 3 Condition HypergeometricPFQRegularized Subscript b 1 -2 Subscript b 2 -2 Subscript b n 1 -2 Subscript b n 2 -1 Subscript b n 3 -1 Subscript b q 1 -1 Subscript b 1 Subscript b 2 Subscript b q z -1 n 2 q z -1 1 z -1 k 0 q -1 Pochhammer n k k -1 PolyLog q -1 k z k 0 n -1 -1 n -1 k Pochhammer q k k -1 PolyLog n -1 k z -1 Binomial n q -1 n Subscript b 1 Subscript b 2 Subscript b q 3 [/itex]

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

 2001-10-29