# §28.4 Fourier Series

## §28.4(i) Definitions

The Fourier series of the periodic Mathieu functions converge absolutely and uniformly on all compact sets in the -plane. For ,

## §28.4(iii) Normalization

28.4.9

Ambiguities in sign are resolved by (28.4.13)–(28.4.16) when , and by continuity for the other values of .

28.4.13
,
,
28.4.14
,
28.4.15
,
28.4.16
.

## §28.4(vi) Behavior for Small

For further terms and expansions see Meixner and Schäfke (1954, p. 122) and McLachlan (1947, §3.33).