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01-12-2019

A remarkable Wronskian with application to critical lengths of cycloidal spaces

Authors: Rachid Ait-Haddou, Marie-Laurence Mazure, Helmut Ruhland

Published in: Calcolo | Issue 4/2019

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Abstract

Recently, Carnicer et al. (Calcolo 54(4):1521–1531, 2017) proved the very elegant and surprising fact that half of the critical length of a cycloidal space coincides with the first positive zero of a spherical Bessel function. Their finding relied in identifying the first positive zero of certain Wronskians. In this paper, we show that these Wronskians admit explicit expressions in terms of spherical Bessel functions. As an application, we recover the above mentioned result.

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Title: A remarkable Wronskian with application to critical lengths of cycloidal spaces
Authors: Rachid Ait-Haddou
Marie-Laurence Mazure
Helmut Ruhland
Publication date: 01-12-2019
Publisher: Springer International Publishing
Published in: Calcolo / Issue 4/2019
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-019-0343-2

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A remarkable Wronskian with application to critical lengths of cycloidal spaces

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