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Relations between integrals arising from Baillie’s identity on trigonometric series
Published online by Cambridge University Press: 15 October 2025
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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.
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- © The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association
References
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