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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving powers of the direct function, trigonometric and exponential functions > Involving powers of cos and exp > Involving ep z cosm(a z) tannu(c z)





http://functions.wolfram.com/01.08.21.0227.01









  


  










Input Form





Integrate[E^(p z) Cos[a z]^m Tan[c z]^\[Nu], z] == ((1 + E^(-2 I c z))^\[Nu] Tan[c z]^\[Nu] ((-(1/p)) E^(p z) AppellF1[(I p)/(2 c), -\[Nu], \[Nu], 1 + (I p)/(2 c), E^(-2 I c z), -E^(-2 I c z)] Binomial[m, m/2] (-1 + Mod[m, 2]) + Sum[((E^((I a (-2 k + m) + p) z) AppellF1[(2 a k - a m + I p)/(2 c), -\[Nu], \[Nu], 1 + (2 a k - a m + I p)/(2 c), E^(-2 I c z), -E^(-2 I c z)])/(I a (-2 k + m) + p) + (E^(((-I) a (-2 k + m) + p) z) AppellF1[(-2 a k + a m + I p)/(2 c), -\[Nu], \[Nu], (2 c - 2 a k + a m + I p)/(2 c), E^(-2 I c z), -E^(-2 I c z)])/((-I) a (-2 k + m) + p)) Binomial[m, k], {k, 0, Floor[(1/2) (-1 + m)]}]))/(2^m (1 - E^(-2 I c z))^\[Nu]) /; 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