# §14.28 Sums

## §14.28(i) Addition Theorem

When , , , and ,

where the branches of the square roots have their principal values when and are continuous when . For this and similar results see Erdélyi et al. (1953a, §3.11).

## §14.28(ii) Heine’s Formula

where and are ellipses with foci at , being properly interior to . The series converges uniformly for outside or on , and within or on .

See §14.18(iv).