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 Tanh

 http://functions.wolfram.com/01.21.21.0185.01

 Input Form

 Integrate[E^(p z) Cos[a z]^m Sinh[c z]^\[Mu] Tanh[c z], z] == ((-(1/(p - c \[Mu]))) E^(p z) Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[c z]^\[Mu] AppellF1[(p - c \[Mu])/(2 c), -1 - \[Mu], 1, (1/2) (2 + p/c - \[Mu]), E^(2 c z), -E^(2 c z)])/ (2^m (1 - E^(2 c z))^\[Mu]) - (Sinh[c z]^\[Mu] Sum[((E^(((-I) a (-2 k + m) + p) z) AppellF1[((-I) a (-2 k + m) + p - c \[Mu])/(2 c), -1 - \[Mu], 1, (1/2) (2 + ((-I) a (-2 k + m) + p)/c - \[Mu]), E^(2 c z), -E^(2 c z)])/((-I) a (-2 k + m) + p - c \[Mu]) + (E^((I a (-2 k + m) + p) z) AppellF1[(I a (-2 k + m) + p - c \[Mu])/ (2 c), -1 - \[Mu], 1, (1/2) (2 + (I a (-2 k + m) + p)/c - \[Mu]), E^(2 c z), -E^(2 c z)])/(I a (-2 k + m) + p - c \[Mu])) Binomial[m, k], {k, 0, Floor[(1/2) (-1 + m)]}])/ (2^m (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 ) sinh μ ( c z ) tanh ( c z ) z - 2 - m p z ( 1 - m mod 2 \$CellContext`m 2 ) sinh μ ( c z ) ( 1 - 2 c z ) - μ p - c 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]]]]] F 1 AppellF1 ( p - c μ 2 c ; - μ - 1 , 1 ; 1 2 ( p c - μ + 2 ) ; 2 c z , - 2 c z ) - 2 - m sinh 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]]]]] ( ( p - a ( m - 2 k ) ) z F 1 AppellF1 ( - a ( m - 2 k ) + p - c μ 2 c ; - μ - 1 , 1 ; 1 2 ( p - a ( m - 2 k ) c - μ + 2 ) ; 2 c z , - 2 c z ) - a ( m - 2 k ) + p - c μ + ( a ( m - 2 k ) + p ) z F 1 AppellF1 ( a ( m - 2 k ) + p - c μ 2 c ; - μ - 1 , 1 ; 1 2 ( a ( m - 2 k ) + p c - μ + 2 ) ; 2 c z , - 2 c z ) a ( m - 2 k ) + p - c μ ) /; m + Condition z p z a z m c z μ c z -1 2 -1 m p z 1 -1 \$CellContext`m 2 c z μ 1 -1 2 c z -1 μ p -1 c μ -1 Binomial m m 2 -1 AppellF1 p -1 c μ 2 c -1 -1 μ -1 1 1 2 p c -1 -1 μ 2 2 c z -1 2 c z -1 2 -1 m c z μ 1 -1 2 c z -1 μ k 0 m -1 2 -1 Binomial m k p -1 a m -1 2 k z AppellF1 -1 a m -1 2 k p -1 c μ 2 c -1 -1 μ -1 1 1 2 p -1 a m -1 2 k c -1 -1 μ 2 2 c z -1 2 c z -1 a m -1 2 k p -1 c μ -1 a m -1 2 k p z AppellF1 a m -1 2 k p -1 c μ 2 c -1 -1 μ -1 1 1 2 a m -1 2 k p c -1 -1 μ 2 2 c z -1 2 c z a m -1 2 k p -1 c μ -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18