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 Cot

 http://functions.wolfram.com/01.09.21.0132.01

 Input Form

 Integrate[z^n Cos[b z]^m Cot[c z], z] == ((-I) Binomial[m, m/2] n! (1 - Mod[m, 2]) (z^(1 + n)/(1 + n)! + 2 E^(2 I c z) Sum[(1/(-j + n)!) ((-1)^j 2^(-1 - j) (I c)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, 2 + j], 2}, {1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, 2 + j]}, E^(2 I c z)]), {j, 0, n}]))/2^m - (I n! Sum[Binomial[m, k] (E^(I b (-2 k + m) z) Sum[(1/(-j + n)!) ((-1)^j (I b (-2 k + m))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[h, 1], \[Ellipsis], Subscript[h, 1 + j], 1}, {1 + Subscript[h, 1], \[Ellipsis], 1 + Subscript[h, 1 + j]}, E^(2 I c z)]), {j, 0, n}] + E^((2 I c + I b (-2 k + m)) z) Sum[(1/(-j + n)!) ((-1)^j (2 I c + I b (-2 k + m))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[i, 1], \[Ellipsis], Subscript[i, 1 + j], 1}, {1 + Subscript[i, 1], \[Ellipsis], 1 + Subscript[i, 1 + j]}, E^(2 I c z)]), {j, 0, n}] + Sum[(1/(-j + n)!) ((-1)^j ((-I) b (-2 k + m))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[p, 1], \[Ellipsis], Subscript[p, 1 + j], 1}, {1 + Subscript[p, 1], \[Ellipsis], 1 + Subscript[p, 1 + j]}, E^(2 I c z)]), {j, 0, n}]/E^(I b (-2 k + m) z) + E^((2 I c - I b (-2 k + m)) z) Sum[(1/(-j + n)!) ((-1)^j (2 I c - I b (-2 k + m))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[q, 1], \[Ellipsis], Subscript[q, 1 + j], 1}, {1 + Subscript[q, 1], \[Ellipsis], 1 + Subscript[q, 1 + j]}, E^(2 I c z)]), {j, 0, n}]), {k, 0, Floor[(1/2) (-1 + m)]}])/2^m /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 2] == 1 && Subscript[h, 1] == Subscript[h, 2] == \[Ellipsis] == Subscript[h, n + 1] == (b (-2 k + m))/(2 c) && Subscript[i, 1] == Subscript[i, 2] == \[Ellipsis] == Subscript[i, n + 1] == (b (-2 k + m) + 2 c)/(2 c) && Subscript[p, 1] == Subscript[p, 2] == \[Ellipsis] == Subscript[p, n + 1] == ((-b) (-2 k + m))/(2 c) && Subscript[q, 1] == Subscript[q, 2] == \[Ellipsis] == Subscript[q, n + 1] == ((-b) (-2 k + m) + 2 c)/(2 c) && Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z n cos m ( b z ) cot ( c z ) z - 2 - m ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["m", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] n ! ( 1 - m mod 2 \$CellContext`m 2 ) ( z n + 1 ( n + 1 ) ! + 2 2 c z j = 0 n ( - 1 ) j 2 - j - 1 ( c ) - j - 1 z n - j ( n - j ) ! j + 3 F j + 2 ( 1 , , 1 , 2 ; 2 , , 2 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["j", "+", "3"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["j", "+", "2"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ], ",", TagBox["2", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox["2", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]], HypergeometricPFQ]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], HypergeometricPFQ] ) - 2 - m n ! 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 Rule Form

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

 2002-12-18