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Tan






Mathematica Notation

Traditional Notation









Elementary Functions > Tan[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving powers of the direct function and a power function > Involving powers of tanh and power > Involving znand linear arguments





http://functions.wolfram.com/01.08.21.0135.01









  


  










Input Form





Integrate[z Tan[c z]^v, z] == (I^v z^2)/2 + (E^(2 I c v z)/(I^v (2 c v))) ((-I) z HypergeometricPFQ[{v, v}, {1 + v}, -E^(2 I c z)] + (1/(2 c v)) HypergeometricPFQ[{v, v, v}, {1 + v, 1 + v}, -E^(2 I c z)]) - ((I^v E^(2 I c z) v)/(2 c)) ((-I) z HypergeometricPFQ[{1, 1, 1 + v}, {2, 2}, -E^(2 I c z)] + (1/(2 c)) HypergeometricPFQ[{1, 1, 1, 1 + v}, {2, 2, 2}, -E^(2 I c z)]) + (E^(I c v z)/(c v)) Binomial[v, v/2] ((-I) z HypergeometricPFQ[{v/2, v}, {1 + v/2}, -E^(2 I c z)] + (1/(c v)) HypergeometricPFQ[{v/2, v/2, v}, {1 + v/2, 1 + v/2}, -E^(2 I c z)]) (1 - Mod[v, 2]) - (1/(I^v (4 c^2))) Sum[(-1)^s Binomial[v, s] ((1/s^2) (-1)^v E^(2 I c s z) (2 I c s z HypergeometricPFQ[{s, v}, {1 + s}, -E^(2 I c z)] - HypergeometricPFQ[{s, s, v}, {1 + s, 1 + s}, -E^(2 I c z)]) - (1/(s - v)^2) (E^(2 I c (-s + v) z) (2 I c (s - v) z HypergeometricPFQ[{v, -s + v}, {1 - s + v}, -E^(2 I c z)] + HypergeometricPFQ[{v, -s + v, -s + v}, {1 - s + v, 1 - s + v}, -E^(2 I c z)]))), {s, 1, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 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