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arXiv · 2508.04582

$h$-Trigonometric B-splines

Fatma Zürnacı-Yetiş·Ron Goldman·Plamen Simeonov
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Abstract

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.

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Fatma Zürnacı-Yetiş, Ron Goldman, Plamen Simeonov. 2025-08-06. $h$-Trigonometric B-splines. https://arxiv.org/abs/2508.04582

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