Dirichlet's lemma states that
![int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi,](/images/equations/DirichletsLemma/NumberedEquation1.svg) |
where the integral kernel is the Dirichlet kernel.
Dirichlet's Lemma
See also
Dirichlet KernelExplore with Wolfram|Alpha
References
Cohn, H. Advanced Number Theory. New York: Dover, p. 37, 1980.Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1101, 2000.Referenced on Wolfram|Alpha
Dirichlet's LemmaCite this as:
Weisstein, Eric W. "Dirichlet's Lemma." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DirichletsLemma.html