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 Csch

 http://functions.wolfram.com/01.23.21.0262.01

 Input Form

 Integrate[E^(p z) Sin[a z]^m Coth[c z]^\[Mu] Csch[c z], z] == ((1/(p - c)) Binomial[m, m/2] 2^(1 - m) E^((p - c) z) (1 - E^(-2 c z))^\[Mu] Coth[c z]^\[Mu] (1 - Mod[m, 2]) 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] + (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[-((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]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

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