2025/10/15 by J. R. Nurcombe
Mathematics · #Iterative Methods for Nonlinear Equations
paper · doi:10.1017/mag.2025.10128
openalex created_date 2025/10/15 · openalex publication_date 2025/10/15 · crossref created 2025/10/15 · crossref issued 2025/11/01 · crossref published 2025/11/01 · crossref published-print 2025/11/01 · crossref published-online 2025/12/09 · openalex updated_date 2026/03/07 · crossref deposited 2026/07/27 · crossref indexed 2026/07/27
Baillie’s identity is (see [1] or [2], p. 240). Its integral analogue, , is not difficult to prove (see Lemma 1, below). In this Article, we prove a generalisation of the latter result (see Theorem 1). Theorems 2 and 3 are extensions, involving in addition, powers of cosines in the integrand. Theorem 4 answers a question raised after the proof of Theorem 1, and Theorem 5 collects together the preceding results in the form of three identities between trigonometric integrals. Theorem 6 gives a further generalisation.