Cotangent: Integration (formula 01.09.21.0251)

Cot

$Mathematica Notation$

Elementary Functions

Cot[z]

Integration

Definite integration

Involving the direct function

http://functions.wolfram.com/01.09.21.0251.01

Input Form

Integrate[(Cot[a t] - 1/(a t)) (z - t)^n, {t, 0, w}] == (z^n/a) (-2 I Pi Floor[3/4 - Arg[a w]/(2 Pi)] - Log[-2 I] - Log[a w] - (I (-1)^n a w^(1 + n))/(z^n (1 + n)) + Sum[(Binomial[n, k] k! PolyLog[1 + k, 1])/(2 I a z)^k, {k, 1, n}] - Sum[(Binomial[n, k]/(k + 1)) (-(w/z))^k (I a w + (k w - n w)/(z + k z)), {k, 0, n - 1}] - Sum[(-(w/z))^k Binomial[n, k] Sum[(Binomial[k, j] j! PolyLog[1 + j, E^(2 I a w)])/(-2 I a w)^j, {j, 0, k}], {k, 0, n}]) /; Element[n, Integers] && n >= 0

Standard Form

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MathML Form

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type='integer'> 1 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> w </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02