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 Csch

 http://functions.wolfram.com/01.23.21.0258.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18