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 Csch

 http://functions.wolfram.com/01.23.21.0256.01

 Input Form

 Integrate[E^(p z) Cos[a z]^m Cosh[c z]^\[Mu] Csch[c z], z] == ((1/(p + c (-1 + \[Mu]))) E^(p z) (1 - E^(-2 c z)) Binomial[m, m/2] Cosh[c z]^\[Mu] Csch[c z] (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)])/ (2^m (1 + E^(-2 c z))^\[Mu]) + (2^(1 - m) Cosh[c z]^\[Mu] Sum[Binomial[m, k] ((E^((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^((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 cos m ( a z ) cosh μ ( c z ) csch ( c z ) z 2 - m p z ( 1 - - 2 c z ) p + c ( μ - 1 ) F 1 AppellF1 ( - μ c - c + p 2 c ; - μ , 1 ; c ( 3 - μ ) - p 2 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]]]]] cosh μ ( c z ) csch ( c z ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 + - 2 c z ) - μ + 2 1 - m - c z cosh μ ( c z ) ( 1 + - 2 c z ) - μ k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( a ( 2 k - m ) + p ) z ( μ - 1 ) c + a ( 2 k - m ) + p F 1 AppellF1 ( - μ c - c + a ( 2 k - m ) + p 2 c ; - μ , 1 ; - a ( 2 k - m ) - p + c ( 3 - μ ) 2 c ; - - 2 c z , - 2 c z ) + ( a ( m - 2 k ) + p ) z ( μ - 1 ) c + a ( m - 2 k ) + p F 1 AppellF1 ( - μ c - c + a ( m - 2 k ) + p 2 c ; - μ , 1 ; - a ( m - 2 k ) - p + c ( 3 - μ ) 2 c ; - - 2 c z , - 2 c z ) ) /; m + Condition z p z a z m c z μ c z 2 -1 m p z 1 -1 -2 c z p c μ -1 -1 AppellF1 -1 μ c -1 c p 2 c -1 -1 μ 1 c 3 -1 μ -1 p 2 c -1 -1 -2 c z -2 c z Binomial m m 2 -1 c z μ c z 1 -1 \$CellContext`m 2 1 -2 c z -1 μ 2 1 -1 m -1 c z c z μ 1 -2 c z -1 μ k 0 m -1 2 -1 Binomial m k a 2 k -1 m p z μ -1 c a 2 k -1 m p -1 AppellF1 -1 μ c -1 c a 2 k -1 m p 2 c -1 -1 μ 1 -1 a 2 k -1 m -1 p c 3 -1 μ 2 c -1 -1 -2 c z -2 c z a m -1 2 k p z μ -1 c a m -1 2 k p -1 AppellF1 -1 μ c -1 c a m -1 2 k p 2 c -1 -1 μ 1 -1 a m -1 2 k -1 p c 3 -1 μ 2 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