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Cot






Mathematica Notation

Traditional Notation









Elementary Functions > Cot[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving powers of sin and exp > Involving ep z sinm(b z)





http://functions.wolfram.com/01.09.21.0138.01









  


  










Input Form





Integrate[E^(p z) Sin[b z]^m Cot[c z], z] == -((1/((2 c - I p) p)) ((Binomial[m, m/2] (E^(p z) (2 I c + p) Hypergeometric2F1[-((I p)/(2 c)), 1, 1 - (I p)/(2 c), E^(2 I c z)] + E^((2 I c + p) z) p Hypergeometric2F1[1 - (I p)/(2 c), 1, 2 - (I p)/(2 c), E^(2 I c z)]) (1 - Mod[m, 2]))/2^m)) - Sum[(-1)^k Binomial[m, k] (E^((I m Pi)/2) ((E^((2 I c - I b (-2 k + m) + p) z) ((-I) b (-2 k + m) + p) Hypergeometric2F1[(2 c + 2 b k - b m - I p)/(2 c), 1, (4 c + 2 b k - b m - I p)/(2 c), E^(2 I c z)] + E^(((-I) b (-2 k + m) + p) z) (2 I c - I b (-2 k + m) + p) Hypergeometric2F1[-((b (-2 k + m) + I p)/(2 c)), 1, (2 c + 2 b k - b m - I p)/(2 c), E^(2 I c z)])/ ((2 c + 2 b k - b m - I p) (I b (2 k - m) + p))) + (E^((2 I c + I b (-2 k + m) + p) z) (I b (-2 k + m) + p) Hypergeometric2F1[(2 c - 2 b k + b m - I p)/(2 c), 1, (4 c - 2 b k + b m - I p)/(2 c), E^(2 I c z)] + E^((I b (-2 k + m) + p) z) (2 I c + I b (-2 k + m) + p) Hypergeometric2F1[(b (-2 k + m) - I p)/(2 c), 1, (2 c - 2 b k + b m - I p)/(2 c), E^(2 I c z)])/ ((2 c + b (-2 k + m) - I p) (I b (-2 k + m) + p))/E^((1/2) I m Pi)), {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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<ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18