# §28.14 Fourier Series

The Fourier series

converge absolutely and uniformly on all compact sets in the -plane. The coefficients satisfy

and the normalization relation

28.14.5

compare (28.12.5). Ambiguities in sign are resolved by (28.14.9) when , and by continuity for other values of .

The rate of convergence is indicated by

For changes of sign of , , and ,

When ,

28.14.9
.

When with () and fixed,