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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving powers of cos and powers of coth > Involving cosm(a z) cothmu(c z) csch(c z)





http://functions.wolfram.com/01.23.21.0221.01









  


  










Input Form





Integrate[Cos[a z]^m Coth[c z]^\[Mu] Csch[c z], z] == (-(1/c)) ((2^(1 - m) (1 - E^(-2 c z))^\[Mu] AppellF1[1/2, -\[Mu], \[Mu] + 1, 3/2, -E^(-2 c z), E^(-2 c z)] Binomial[m, m/2] Coth[c z]^\[Mu] (1 - Mod[m, 2]))/(E^(c z) (1 + E^(-2 c z))^\[Mu])) + (2^(1 - m) (1 - E^(-2 c z))^\[Mu] Coth[c z]^\[Mu] Sum[Binomial[m, k] ((1/(I a (2 k - m) - c)) (E^(I a (2 k - m) z) AppellF1[-((I a (2 k - m) - c)/(2 c)), -\[Mu], \[Mu] + 1, (1/2) (3 - (I a (2 k - m))/c), -E^(-2 c z), E^(-2 c z)]) + (E^(I a (-2 k + m) z) AppellF1[-((I a (-2 k + m) - c)/(2 c)), -\[Mu], \[Mu] + 1, (1/2) (3 - (I a (-2 k + m))/c), -E^(-2 c z), E^(-2 c z)])/(I a (-2 k + m) - 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







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Rule Form





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





2002-12-18