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 Csch

 http://functions.wolfram.com/01.23.21.0239.01

 Input Form

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

 Standard Form

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 MathML Form

 z n - c z ( 2 q + 1 ) tanh ( c z ) csch ( c z ) z 2 n ! ( ( - 1 ) q z n + 1 ( n + 1 ) ! + ( - 1 ) q 2 c z j = 0 n ( - 2 c ) - j - 1 z n - j ( 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[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], HypergeometricPFQ]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]] - j = 0 n k = 0 q - 1 ( - 1 ) k 2 c ( k - q ) z ( 2 c ( q - k ) ) - j - 1 z n - j ( n - j ) ! ) /; n q + Condition z z n -1 c z 2 q 1 c z c z 2 n -1 q z n 1 n 1 -1 -1 q 2 c z j 0 n -2 c -1 j -1 z n -1 j n -1 j -1 HypergeometricPFQ 1 1 1 2 2 -1 2 c z -1 k 0 q -1 j 0 n -1 k 2 c k -1 q z 2 c q -1 k -1 j -1 z n -1 j n -1 j -1 n q SuperPlus [/itex]

 Rule Form

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

 2002-12-18