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Csc






Mathematica Notation

Traditional Notation









Elementary Functions > Csc[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving powers of the direct function and trigonometric functions > Involving powers of cos > Involving cosm(b z)





http://functions.wolfram.com/01.10.21.0130.01









  


  










Input Form





Integrate[Cos[b z]^m Csc[c z]^\[Nu], z] == ((-I) (1 - E^(2 I c z))^\[Nu] Binomial[m, m/2] Csc[c z]^\[Nu] (1 - Mod[m, 2]) (HypergeometricPFQ[{\[Nu]/2, \[Nu]}, {1 + \[Nu]/2}, E^(2 I c z)]/(c \[Nu])))/2^m - (I (1 - E^(2 I c z))^\[Nu] Csc[c z]^\[Nu] Sum[Binomial[m, s] ((E^(I b (m - 2 s) z) Hypergeometric2F1[ (b (m - 2 s) + c \[Nu])/(2 c), \[Nu], 1 + (b (m - 2 s) + c \[Nu])/ (2 c), E^(2 I c z)])/(b (m - 2 s) + c \[Nu]) + Hypergeometric2F1[((-b) (m - 2 s) + c \[Nu])/(2 c), \[Nu], 1 + ((-b) (m - 2 s) + c \[Nu])/(2 c), E^(2 I c z)]/ E^(I b (m - 2 s) z)/((-b) (m - 2 s) + c \[Nu])), {s, 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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Rule Form





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





2002-12-18