, 56:45 | Cite as

A remarkable Wronskian with application to critical lengths of cycloidal spaces

  • Rachid Ait-HaddouEmail author
  • Marie-Laurence Mazure
  • Helmut Ruhland


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.


Extended Chebyshev spaces Critical lengths Bessel functions Cycloidal spaces 

Mathematics Subject Classification

41A05 41A10 41A29 65D05 65D17 65D18 



The authors are extremely grateful to the referees for their interesting suggestions which truly helped them improve this article.


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Copyright information

© Istituto di Informatica e Telematica (IIT) 2019

Authors and Affiliations

  • Rachid Ait-Haddou
    • 1
    Email author
  • Marie-Laurence Mazure
    • 2
  • Helmut Ruhland
    • 3
  1. 1.Cybermedia Center 6FOsaka UniversityToyonakaJapan
  2. 2.Laboratoire Jean Kuntzmann, CNRSUniversité Grenoble AlpesGrenobleFrance
  3. 3.HavanaCuba

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