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 Csch

 http://functions.wolfram.com/01.23.21.0250.01

 Input Form

 Integrate[E^(p z) Cos[a z]^m Sinh[c z]^\[Mu] Csch[c z], z] == (1/(c + p - c \[Mu])) ((2^(1 - m) E^((c + p) z) Binomial[m, m/2] Hypergeometric2F1[(c + p - c \[Mu])/(2 c), 1 - \[Mu], (3 c + p - c \[Mu])/(2 c), E^(2 c z)] (-1 + Mod[m, 2]) Sinh[c z]^\[Mu])/(1 - E^(2 c z))^\[Mu]) - (2^(1 - m) E^(c z) Sinh[c z]^\[Mu] Sum[Binomial[m, k] (E^((I a (2 k - m) + p) z) (Hypergeometric2F1[(I a (2 k - m) + p - c \[Mu] + c)/(2 c), -\[Mu] + 1, (I a (2 k - m) + p + c (3 - \[Mu]))/(2 c), E^(2 c z)]/ (I a (2 k - m) + p + c (-\[Mu] + 1))) + E^((I a (-2 k + m) + p) z) (Hypergeometric2F1[(I a (-2 k + m) + p - c \[Mu] + c)/(2 c), -\[Mu] + 1, (I a (-2 k + m) + p + c (3 - \[Mu]))/(2 c), E^(2 c z)]/ (I a (-2 k + m) + p + c (-\[Mu] + 1)))), {k, 0, Floor[(1/2) (-1 + m)]}])/(1 - E^(2 c z))^\[Mu] /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 p z cos m ( a z ) sinh μ ( c z ) csch ( c z ) z 1 - μ c + c + p 2 1 - m ( c + p ) z ( 1 - 2 c z ) - μ ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] 2 F 1 ( - μ c + c + p 2 c , 1 - μ ; - μ c + 3 c + p 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[Mu]"]], " ", "c"]], "+", "c", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox[RowBox[List["1", "-", "\[Mu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[Mu]"]], " ", "c"]], "+", RowBox[List["3", " ", "c"]], "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ( m mod 2 \$CellContext`m 2 - 1 ) sinh μ ( c z ) - 2 1 - m c z ( 1 - 2 c z ) - μ sinh μ ( c z ) k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( a ( 2 k - m ) + p ) z 2 F 1 ( a ( 2 k - m ) + p - c μ + c 2 c , 1 - μ ; a ( 2 k - m ) + p + c ( - μ + 3 ) 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["a", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p", "-", RowBox[List["c", " ", "\[Mu]"]], "+", "c"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox[RowBox[List["1", "-", "\[Mu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["a", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Mu]"]], "+", "3"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] a ( 2 k - m ) + p + c ( 1 - μ ) + ( a ( m - 2 k ) + p ) z 2 F 1 ( a ( m - 2 k ) + p - c μ + c 2 c , 1 - μ ; a ( m - 2 k ) + p + c ( - μ + 3 ) 2 c ; 2 c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["a", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "-", RowBox[List["c", " ", "\[Mu]"]], "+", "c"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox[RowBox[List["1", "-", "\[Mu]"]], Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["a", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "k"]]]], ")"]]]], "+", "p", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Mu]"]], "+", "3"]], ")"]]]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] a ( m - 2 k ) + p + c ( 1 - μ ) ) /; m + Condition z p z a z m c z μ c z 1 -1 μ c c p -1 2 1 -1 m c p z 1 -1 2 c z -1 μ Binomial m m 2 -1 Hypergeometric2F1 -1 μ c c p 2 c -1 1 -1 μ -1 μ c 3 c p 2 c -1 2 c z \$CellContext`m 2 -1 c z μ -1 2 1 -1 m c z 1 -1 2 c z -1 μ c z μ k 0 m -1 2 -1 Binomial m k a 2 k -1 m p z Hypergeometric2F1 a 2 k -1 m p -1 c μ c 2 c -1 1 -1 μ a 2 k -1 m p c -1 μ 3 2 c -1 2 c z a 2 k -1 m p c 1 -1 μ -1 a m -1 2 k p z Hypergeometric2F1 a m -1 2 k p -1 c μ c 2 c -1 1 -1 μ a m -1 2 k p c -1 μ 3 2 c -1 2 c z a m -1 2 k p c 1 -1 μ -1 m SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["a_", " ", "z_"]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "\[Mu]_"], " ", RowBox[List["Csch", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "m"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], ")"]], RowBox[List["-", "\[Mu]"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18