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 Csch

 http://functions.wolfram.com/01.23.21.0218.01

 Input Form

 Integrate[Sin[a z]^m Coth[c z]^\[Mu] Csch[c z], z] == (-((2^(1 - m) (1 - E^(-2 c z))^\[Mu] Binomial[m, m/2] Coth[c z]^\[Mu])/ (E^(c z) (1 + E^(-2 c z))^\[Mu] c))) AppellF1[1/2, -\[Mu], \[Mu] + 1, 3/2, -E^(-2 c z), E^(-2 c z)] (1 - Mod[m, 2]) + (2^(1 - m) (1 - E^(-2 c z))^\[Mu] Coth[c z]^\[Mu] Sum[(-1)^k ((1/(I a (2 k - m) - c)) (E^((I m Pi)/2 + I a (2 k - m) z) AppellF1[-((I a (2 k - m) - c)/(2 c)), -\[Mu], \[Mu] + 1, (1/2) (3 - (I a (2 k - m))/c), -E^(-2 c z), E^(-2 c z)]) + (E^((-(1/2)) I m Pi + I a (-2 k + m) z) AppellF1[ -((I a (-2 k + m) - c)/(2 c)), -\[Mu], \[Mu] + 1, (1/2) (3 - (I a (-2 k + m))/c), -E^(-2 c z), E^(-2 c z)])/ (I a (-2 k + m) - c)) Binomial[m, k], {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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 MathML Form

 sin m ( a z ) coth μ ( c z ) csch ( c z ) z 2 1 - m - c z ( 1 - - 2 c z ) μ ( 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]]]]] ( π m 2 + a ( 2 k - m ) z F 1 AppellF1 ( - a ( 2 k - m ) - c 2 c ; - μ , μ + 1 ; 1 2 ( 3 - a ( 2 k - m ) c ) ; - - 2 c z , - 2 c z ) a ( 2 k - m ) - c + a ( m - 2 k ) z - m π 2 F 1 AppellF1 ( - a ( m - 2 k ) - c 2 c ; - μ , μ + 1 ; 1 2 ( 3 - a ( m - 2 k ) c ) ; - - 2 c z , - 2 c z ) a ( m - 2 k ) - c ) - 2 1 - m - c z ( 1 - - 2 c z ) μ ( 1 + - 2 c z ) - μ coth μ ( c z ) c ( 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]]]]] F 1 AppellF1 ( 1 2 ; - μ , μ + 1 ; 3 2 ; - - 2 c z , - 2 c z ) ( 1 - m mod 2 \$CellContext`m 2 ) /; m + Condition z a z m c z μ c z 2 1 -1 m -1 c z 1 -1 -2 c z μ 1 -2 c z -1 μ c z μ k 0 m -1 2 -1 -1 k Binomial m k m 2 -1 a 2 k -1 m z AppellF1 -1 a 2 k -1 m -1 c 2 c -1 -1 μ μ 1 1 2 3 -1 a 2 k -1 m c -1 -1 -2 c z -2 c z a 2 k -1 m -1 c -1 a m -1 2 k z -1 m 2 -1 AppellF1 -1 a m -1 2 k -1 c 2 c -1 -1 μ μ 1 1 2 3 -1 a m -1 2 k c -1 -1 -2 c z -2 c z a m -1 2 k -1 c -1 -1 2 1 -1 m -1 c z 1 -1 -2 c z μ 1 -2 c z -1 μ c z μ c -1 Binomial m m 2 -1 AppellF1 1 2 -1 μ μ 1 3 2 -1 -2 c z -2 c z 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