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 HypergeometricPFQRegularized

 http://functions.wolfram.com/07.32.03.0036.01

 Input Form

 HypergeometricPFQRegularized[{-n, Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[a, 2] - 1, \[Ellipsis], Subscript[a, q + 1] - 1}, 1] == S[q, n]/Gamma[a - 1]^q /; Subscript[a, 2] == Subscript[a, 3] == \[Ellipsis] == Subscript[a, q + 1] == a && S[q, 0] == 1 && (S[q, n] == 0 /; n > q) && S[q, q] == q/(1 - a)^q && S[q, q - 1] == (q! ((3 - q)/2 - a))/(1 - a)^q && S[q, q - 2] == (q!/((1 - a)^q 24)) (12 (a + q - 3) (a - 1) + (q - 2) (3 q - 5)) && S[q, n] == ((a + n - 1)/(a - 1)) S[q - 1, n] - (n/(a - 1)) S[q - 1, n - 1] && Element[n, Integers] && n > 0

 Standard Form

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 MathML Form

 q + 1 F ~ q ( - n , a 2 , , a q + 1 ; a 2 - 1 , , a q + 1 - 1 ; 1 ) 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[RowBox[List["-", "n"]], ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", RowBox[List["q", "+", "1"]]], ";", RowBox[List[SubscriptBox["a", "2"], "-", "1"]]]], ",", "\[Ellipsis]", ",", RowBox[List[RowBox[List[SubscriptBox["a", RowBox[List["q", "+", "1"]]], "-", "1"]], ";", TagBox["1", HypergeometricPFQ, Rule[Editable, True]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] S ( q , n ) Γ ( a - 1 ) q /; a 2 a 3 a q + 1 a S ( q , 0 ) 1 ( S ( q , n ) 0 /; n > q ) S ( q , q ) ( 1 - a ) - q q S ( q , q - 1 ) ( 1 - a ) - q q ! ( 3 - q 2 - a ) S ( q , q - 2 ) q ! 24 ( 1 - a ) - q ( ( 3 q - 5 ) ( q - 2 ) + 12 ( a + q - 3 ) ( a - 1 ) ) S ( q , n ) a + n - 1 a - 1 S ( q - 1 , n ) - n a - 1 S ( q - 1 , n - 1 ) n + q + 1 F ~ q ( - n , a 2 , , a q + 1 ; a 2 - 1 , , a q + 1 - 1 ; 1 ) 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[RowBox[List["-", "n"]], ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", RowBox[List["q", "+", "1"]]], ";", RowBox[List[SubscriptBox["a", "2"], "-", "1"]]]], ",", "\[Ellipsis]", ",", RowBox[List[RowBox[List[SubscriptBox["a", RowBox[List["q", "+", "1"]]], "-", "1"]], ";", TagBox["1", HypergeometricPFQ, Rule[Editable, True]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] S ( q , n ) Γ ( a - 1 ) q /; a 2 a 3 a q + 1 a S ( q , 0 ) 1 ( S ( q , n ) 0 /; n > q ) S ( q , q ) ( 1 - a ) - q q S ( q , q - 1 ) ( 1 - a ) - q q ! ( 3 - q 2 - a ) S ( q , q - 2 ) q ! 24 ( 1 - a ) - q ( ( 3 q - 5 ) ( q - 2 ) + 12 ( a + q - 3 ) ( a - 1 ) ) S ( q , n ) a + n - 1 a - 1 S ( q - 1 , n ) - n a - 1 S ( q - 1 , n - 1 ) n + [/itex]

 Rule Form

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

 2001-10-29