A remarkable Wronskian with application to critical lengths of cycloidal spaces
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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.
KeywordsExtended Chebyshev spaces Critical lengths Bessel functions Cycloidal spaces
Mathematics Subject Classification41A05 41A10 41A29 65D05 65D17 65D18
The authors are extremely grateful to the referees for their interesting suggestions which truly helped them improve this article.
- 1.Beccari, C.V., Casciola G., Mazure. M.-L.: Critical length: an alternative approach, preprintGoogle Scholar