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Dirichlet's Lemma

\int_0^\pi {\sin[(n+{\textstyle{1\over 2}})x]\over 2\sin({\textstyle{1\over 2}}x)}\,dx={\textstyle{1\over 2}}\pi,

where the Kernel is the Dirichlet Kernel.


Cohn, H. Advanced Number Theory. New York: Dover, p. 37, 1980.

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1101, 1979.

© 1996-9 Eric W. Weisstein