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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving powers of sin and powers of sinh > Involving sinm(a z) sinhu(b z) tanh(c z)





http://functions.wolfram.com/01.21.21.0161.01









  


  










Input Form





Integrate[Sin[a z]^m Sinh[c z]^\[Mu] Tanh[c z], z] == (1/(c \[Mu])) ((AppellF1[-(\[Mu]/2), -1 - \[Mu], 1, (2 - \[Mu])/2, E^(2 c z), -E^(2 c z)] Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[c z]^\[Mu])/(2^m (1 - E^(2 c z))^\[Mu])) - (Sinh[c z]^\[Mu] Sum[(-1)^k ((E^((I m Pi)/2 - I a (-2 k + m) z) AppellF1[((-I) a (-2 k + m) - c \[Mu])/(2 c), -1 - \[Mu], 1, (1/2) (2 - (I a (-2 k + m))/c - \[Mu]), E^(2 c z), -E^(2 c z)])/ ((-I) a (-2 k + m) - c \[Mu]) + (E^((-(1/2)) I m Pi + I a (-2 k + m) z) AppellF1[ (I a (-2 k + m) - c \[Mu])/(2 c), -1 - \[Mu], 1, (1/2) (2 + (I a (-2 k + m))/c - \[Mu]), E^(2 c z), -E^(2 c z)])/ (I a (-2 k + m) - 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







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Rule Form





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





2002-12-18





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