§14.28 Sums
Contents
§14.28(i) Addition Theorem
When , , , and ,
14.28.1
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
14.28.2, ,
where and are ellipses with foci at , being properly interior to . The series converges uniformly for outside or on , and within or on .
§14.28(iii) Other Sums
See §14.18(iv).