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 Sech

 http://functions.wolfram.com/01.24.21.0260.01

 Input Form

 Integrate[E^(p z) Sin[a z]^m Coth[c z]^\[Mu] Sech[c z], z] == (1/(-c + p)) ((2^(1 - m) E^((p - c) z) (1 - E^(-2 c z))^\[Mu] AppellF1[-((-c + p)/(2 c)), 1 - \[Mu], \[Mu], (1/2) (3 - p/c), -E^(-2 c z), E^(-2 c z)] Binomial[m, m/2] Coth[c z]^\[Mu] (1 - Mod[m, 2]))/(1 + E^(-2 c z))^\[Mu]) + (2^(1 - m) (1 - E^(-2 c z))^\[Mu] Coth[c z]^\[Mu] Sum[(-1)^k Binomial[m, k] ((E^((I m Pi)/2 + ((-I) a (-2 k + m) + p) z) AppellF1[-((-c - I a (-2 k + m) + p)/(2 c)), 1 - \[Mu], \[Mu], (1/2) (3 - ((-I) a (-2 k + m) + p)/c), -E^(-2 c z), E^(-2 c z)])/ (-c - I a (-2 k + m) + p) + (E^((-(1/2)) I m Pi + (I a (-2 k + m) + p) z) AppellF1[-((-c + I a (-2 k + m) + p)/(2 c)), 1 - \[Mu], \[Mu], (1/2) (3 - (I a (-2 k + m) + p)/c), -E^(-2 c z), E^(-2 c z)])/ (-c + I a (-2 k + m) + p)), {k, 0, Floor[(1/2) (-1 + m)]}])/ (E^(c z) (1 + E^(-2 c z))^\[Mu]) /; Element[m, Integers] && m > 0

 Standard Form

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")"]]]], "+", "p"]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z sin m ( a z ) coth μ ( c z ) sech ( c z ) z 2 1 - m - c z ( 1 - - 2 c z ) μ coth μ ( c z ) ( k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - c + a ( m - 2 k ) + p ( ( a ( m - 2 k ) + p ) z - m π 2 F 1 AppellF1 ( - - c + a ( m - 2 k ) + p 2 c ; 1 - μ , μ ; 1 2 ( 3 - a ( m - 2 k ) + p c ) ; - - 2 c z , - 2 c z ) ) + 1 - c - a ( m - 2 k ) + p ( π m 2 + ( p - a ( m - 2 k ) ) z F 1 AppellF1 ( - - c - a ( m - 2 k ) + p 2 c ; 1 - μ , μ ; 1 2 ( 3 - p - a ( m - 2 k ) c ) ; - - 2 c z , - 2 c z ) ) ) ) ( 1 + - 2 c z ) - μ + 1 p - c ( 2 1 - m ( p - c ) z ( 1 - - 2 c z ) μ ( 1 + - 2 c z ) - μ F 1 AppellF1 ( - p - c 2 c ; 1 - μ , μ ; 1 2 ( 3 - p c ) ; - - 2 c z , - 2 c z ) ( 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]]]]] coth μ ( c z ) ( 1 - m mod 2 \$CellContext`m 2 ) ) /; m + Condition z p z a z m c z μ c z 2 1 -1 m -1 c z 1 -1 -2 c z μ c z μ k 0 m -1 2 -1 -1 k Binomial m k 1 -1 c a m -1 2 k p -1 a m -1 2 k p z -1 m 2 -1 AppellF1 -1 -1 c a m -1 2 k p 2 c -1 1 -1 μ μ 1 2 3 -1 a m -1 2 k p c -1 -1 -2 c z -2 c z 1 -1 c -1 a m -1 2 k p -1 m 2 -1 p -1 a m -1 2 k z AppellF1 -1 -1 c -1 a m -1 2 k p 2 c -1 1 -1 μ μ 1 2 3 -1 p -1 a m -1 2 k c -1 -1 -2 c z -2 c z 1 -2 c z -1 μ 1 p -1 c -1 2 1 -1 m p -1 c z 1 -1 -2 c z μ 1 -2 c z -1 μ AppellF1 -1 p -1 c 2 c -1 1 -1 μ μ 1 2 3 -1 p c -1 -1 -2 c z -2 c z Binomial m m 2 -1 c z μ 1 -1 \$CellContext`m 2 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18