Cosecant: Integration (formula 01.10.21.0050)

Csc

$Mathematica Notation$

Elementary Functions

Csc[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving power of cos

Involving cos^m(b z)

http://functions.wolfram.com/01.10.21.0050.01

Input Form

Integrate[Cos[b z]^m Csc[c z], z] == (2^(1 - m) ArcTanh[E^(I c z)] Binomial[m, m/2] (-1 + Mod[m, 2]))/c - 2^(1 - m) E^(I c z) Sum[Binomial[m, s] ((E^(I b (m - 2 s) z) HypergeometricPFQ[{(b (m - 2 s) + c)/(2 c), 1}, {1 + (b (m - 2 s) + c)/(2 c)}, E^(2 I c z)])/(b (m - 2 s) + c) + HypergeometricPFQ[{((-b) (m - 2 s) + c)/(2 c), 1}, {1 + ((-b) (m - 2 s) + c)/(2 c)}, E^(2 I c z)]/E^(I b (m - 2 s) z)/ ((-b) (m - 2 s) + c)), {s, 0, Floor[(1/2) (-1 + 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