A remarkable Wronskian with application to critical lengths of cycloidal spaces

Rachid Ait-Haddou; Marie Laurence Mazure; Helmut Ruhland

doi:10.1007/s10092-019-0343-2

A remarkable Wronskian with application to critical lengths of cycloidal spaces

Rachid Ait-Haddou^*
, Marie Laurence Mazure
, Helmut Ruhland

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Article number	45
Journal	Calcolo
Volume	56
Issue number	4
DOIs	https://doi.org/10.1007/s10092-019-0343-2
State	Published - 1 Dec 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019, Istituto di Informatica e Telematica (IIT).

Keywords

Bessel functions
Critical lengths
Cycloidal spaces
Extended Chebyshev spaces

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

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10.1007/s10092-019-0343-2

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title = "A remarkable Wronskian with application to critical lengths of cycloidal spaces",

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.",

keywords = "Bessel functions, Critical lengths, Cycloidal spaces, Extended Chebyshev spaces",

author = "Rachid Ait-Haddou and Mazure, \{Marie Laurence\} and Helmut Ruhland",

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doi = "10.1007/s10092-019-0343-2",

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AU - Ait-Haddou, Rachid

AU - Mazure, Marie Laurence

AU - Ruhland, Helmut

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Bessel functions

KW - Critical lengths

KW - Cycloidal spaces

KW - Extended Chebyshev spaces

UR - https://www.scopus.com/pages/publications/85074172009

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JF - Calcolo

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M1 - 45

ER -

A remarkable Wronskian with application to critical lengths of cycloidal spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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