Abstract:We present a novel and non-standard derivation of the Bickley-Naylor functions $Ki_n, n\in\mathbb{N}_0.$ A $3\times 3$ system of equations is developed, the solution of which yields new explicit expressions for the Bickley-Naylor functions $Ki_2$, $Ki_3$, and $Ki_4$. Using a recurrence relation, expressions follow for any other order of Bickley-Naylor functions. We then characterize the infinite set of $Ki_n, n\in\mathbb{N}_0$ as a four-dimensional span of modified Bessel and Struve functions over the ring of real polynomials, thus providing a new computational and modeling tool for studying and applying the Bickley-Naylor functions
From: Bourama Toni [view email]
[v1]
Wed, 24 Jun 2026 22:11:56 UTC (21 KB)
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