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 HypergeometricPFQRegularized

 http://functions.wolfram.com/07.32.03.0020.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29