2025/08/06 by Zürnacı-Yetiş, Fatma, Goldman, Ron, Simeonov, Plamen
#41A15 #65D017 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2508.04582
We introduce discrete analogues of the exponential, sine, and cosine functions. Then using a discrete trigonometric version of a non-polynomial divided difference, we define discrete analogues of the trigonometric B-splines. We derive a two-term recurrence relation, a two-term formula for the discrete derivative, and two variants of the Marsden identity for these discrete trigonometric B-splines. Since the classical exponential, sine, and cosine functions are limiting cases of their discrete analogues, we conclude that many of the standard results for classical polynomial B-splines extend naturally both to trigonometric B-splines and to discrete trigonometric B-splines.