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 HypergeometricPFQRegularized

 http://functions.wolfram.com/07.32.03.0040.01

 Input Form

 HypergeometricPFQRegularized[{-n, a/(q + 1), (a + 1)/(q + 1), \[Ellipsis], (a + q)/(q + 1), b/q, (b + 1)/q, \[Ellipsis], (b + q - 1)/q}, {a/q, (a + 1)/q, \[Ellipsis], (a + q - 1)/q, (1 + b - n)/(q + 1), (2 + b - n)/(q + 1), \[Ellipsis], (q + 1 + b - n)/(q + 1)}, 1] == ((-1)^n (2 Pi)^(1/2 - q) q^(a - 1/2) (1 + q)^(1/2 + b - n) Pochhammer[a - b, n])/((b + n q) Gamma[a] Gamma[b]) /; Element[n, Integers] && n > 0

 Standard Form

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 MathML Form

 2 q + 2 F ~ 2 q + 1 ( - n , a q + 1 , a + 1 q + 1 , , a + q q + 1 , b q , b + 1 q , , b + q - 1 q ; a q , a + 1 q , , a + q - 1 q , b - n + 1 q + 1 , b - n + 2 q + 1 , , b - n + q + 1 q + 1 ; 1 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List[RowBox[List["2", "q"]], "+", "2"]], TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox[RowBox[List[RowBox[List["2", "q"]], "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", "n"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["a", RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "1"]], RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "q"]], RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["b", "+", "1"]], "q"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", RowBox[List[TagBox[FractionBox[RowBox[List["b", "+", "q", "-", "1"]], "q"], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["a", "q"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "1"]], "q"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "q", "-", "1"]], "q"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["b", "-", "n", "+", "1"]], RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["b", "-", "n", "+", "2"]], RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["b", "-", "n", "+", "q", "+", "1"]], RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["1", HypergeometricPFQ, Rule[Editable, True]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] ( - 1 ) n ( 2 π ) 1 2 - q q a - 1 2 ( q + 1 ) b - n + 1 2 ( a - b ) n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "n"], Pochhammer] ( b + n q ) Γ ( a ) Γ ( b ) /; n + Condition HypergeometricPFQ -1 n a q 1 -1 a 1 q 1 -1 -1 n 2 1 2 -1 q q a -1 1 2 q 1 b -1 n 1 2 Pochhammer a -1 b n b n q Gamma a Gamma b -1 n SuperPlus [/itex]

 Rule Form

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

 2001-10-29