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 Csch

 http://functions.wolfram.com/01.23.21.0253.01

 Input Form

 Integrate[E^(p z) Sin[a z]^m Cosh[c z]^\[Mu] Csch[c z], z] == ((1/(p + c (\[Mu] - 1))) 2^(1 - m) E^((p - c) z) Binomial[m, m/2] Cosh[c z]^\[Mu] (1 - Mod[m, 2]) AppellF1[-((p + c \[Mu] - c)/(2 c)), -\[Mu], 1, (-p + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/ (1 + E^(-2 c z))^\[Mu] + (2^(1 - m) Cosh[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 \[Mu] - c)/(2 c)), -\[Mu], 1, ((-I) a (2 k - m) - p + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/(I a (2 k - m) + p + c (\[Mu] - 1)) + (E^((-(1/2)) I m Pi + (I a (-2 k + m) + p) z) AppellF1[-((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), E^(-2 c z)])/(I a (-2 k + m) + p + c (\[Mu] - 1))), {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 ) cosh μ ( c z ) csch 1 ( c z ) z 1 ( μ - 1 ) c + p 2 1 - m ( p - c ) 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]]]]] cosh μ ( c z ) ( 1 - m mod 2 \$CellContext`m 2 ) F 1 AppellF1 ( - μ c - c + p 2 c ; - μ , 1 ; c ( - μ + 3 ) - p 2 c ; - - 2 c z , - 2 c z ) + 2 1 - m - c z ( 1 + - 2 c z ) - μ cosh 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 ) + p ) z F 1 AppellF1 ( - a ( 2 k - m ) + p + c μ - c 2 c ; - μ , 1 ; - a ( 2 k - m ) - p + c ( - μ + 3 ) 2 c ; - - 2 c z , - 2 c z ) ) / ( a ( 2 k - m ) + p + c ( μ - 1 ) ) + ( ( a ( m - 2 k ) + p ) z - m π 2 F 1 AppellF1 ( - a ( m - 2 k ) + p + c μ - c 2 c ; - μ , 1 ; - a ( m - 2 k ) - p + c ( - μ + 3 ) 2 c ; - - 2 c z , - 2 c z ) ) / ( a ( m - 2 k ) + p + c ( μ - 1 ) ) ) /; m + Condition z p z a z m c z μ c z 1 1 μ -1 c p -1 2 1 -1 m p -1 c z 1 -2 c z -1 μ Binomial m m 2 -1 c z μ 1 -1 \$CellContext`m 2 AppellF1 -1 μ c -1 c p 2 c -1 -1 μ 1 c -1 μ 3 -1 p 2 c -1 -1 -2 c z -2 c z 2 1 -1 m -1 c z 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 p z AppellF1 -1 a 2 k -1 m p c μ -1 c 2 c -1 -1 μ 1 -1 a 2 k -1 m -1 p c -1 μ 3 2 c -1 -1 -2 c z -2 c z a 2 k -1 m p c μ -1 -1 a m -1 2 k p z -1 m 2 -1 AppellF1 -1 a m -1 2 k p c μ -1 c 2 c -1 -1 μ 1 -1 a m -1 2 k -1 p c -1 μ 3 2 c -1 -1 -2 c z -2 c z a m -1 2 k p c μ -1 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18