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 Csc

 http://functions.wolfram.com/01.10.21.0070.01

 Input Form

 Integrate[z^n E^(p z) Cos[a + b z] Csc[c z], z] == (-I) E^((-I) a + ((-I) b + I c + p) z) n! Sum[(1/(-j + n)!) ((-1)^j ((-I) b + I c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis], Subscript[b, j + 1], 1}, {1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, j + 1]}, E^(2 I c z)]), {j, 0, n}] - I E^(I a + (I b + I c + p) z) n! Sum[(1/(-j + n)!) ((-1)^j (I b + I c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[c, 1], \[Ellipsis], Subscript[c, j + 1], 1}, {1 + Subscript[c, 1], \[Ellipsis], 1 + Subscript[c, j + 1]}, E^(2 I c z)]), {j, 0, n}] /; Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == (c - b - I p)/(2 c) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (c + b - I p)/(2 c) && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos ( a + b z ) csc ( c z ) z - - a + ( c - b + p ) z n ! j = 0 n ( - 1 ) j ( c - b + p ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( c - b - p 2 c , , c - b - p 2 c , 1 ; c - b - p 2 c + 1 , , c - b - p 2 c + 1 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["j", "+", "2"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["j", "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["c", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List["c", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["c", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List["c", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], 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] - a + ( c + b + p ) z n ! j = 0 n ( - 1 ) j ( c + b + p ) - j - 1 z n - j ( n - j ) ! j + 2 F j + 1 ( c + b - p 2 c , , c + b - p 2 c , 1 ; c + b - p 2 c + 1 , , c + b - p 2 c + 1 ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["j", "+", "2"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["j", "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["c", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox[RowBox[List["c", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["c", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox[RowBox[List["c", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], "+", "1"]], 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] /; n Condition z z n p z a b z c z -1 -1 a c -1 b p z n j 0 n -1 j c -1 b p -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ c -1 b -1 p 2 c -1 c -1 b -1 p 2 c -1 1 c -1 b -1 p 2 c -1 1 c -1 b -1 p 2 c -1 1 2 c z -1 a c b p z n j 0 n -1 j c b p -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ c b -1 p 2 c -1 c b -1 p 2 c -1 1 c b -1 p 2 c -1 1 c b -1 p 2 c -1 1 2 c z n [/itex]

 Rule Form

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

 2002-12-18