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 Csch

 http://functions.wolfram.com/01.23.21.0234.01

 Input Form

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

 Standard Form

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 MathML Form

 z n ( b - c ) z cosh ( b z ) csch ( c z ) z - z n + 1 n + 1 - 2 c z n ! j = 0 n ( - 1 ) j z n - j ( 2 c ) - j - 1 ( n - j ) ! j + 2 F j + 1 ( 1 , , 1 , 1 ; 2 , , 2 ; 2 c z ) 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["1", HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ], ",", TagBox["1", 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", " ", "c", " ", "z"]]], HypergeometricPFQ]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]] - 2 b z n ! j = 0 n ( - 1 ) j z n - j ( 2 b ) - j - 1 ( n - j ) ! j + 2 F j + 1 ( b c , , b c , 1 ; b c + 1 , , b c + 1 ; 2 c z ) 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["b", "c"], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[FractionBox["b", "c"], HypergeometricPFQ], ",", TagBox["1", HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["b", "c"], "+", "1"]], HypergeometricPFQ], ",", TagBox["\[Ellipsis]", HypergeometricPFQ], ",", TagBox[RowBox[List[FractionBox["b", "c"], "+", "1"]], HypergeometricPFQ]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], HypergeometricPFQ]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]] /; n Condition z z n b -1 c z b z c z -1 z n 1 n 1 -1 -1 2 c z n j 0 n -1 j z n -1 j 2 c -1 j -1 n -1 j -1 HypergeometricPFQ 1 1 1 2 2 2 c z -1 2 b z n j 0 n -1 j z n -1 j 2 b -1 j -1 n -1 j -1 HypergeometricPFQ b c -1 b c -1 1 b c -1 1 b 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