Abstract
Cycloidal spaces are generated by the trigonometric polynomials of degree one and algebraic polynomials. The critical length of a cycloidal space is the supremum of the lengths of the intervals on which the Hermite interpolation problems are unisolvent. The critical length is related with the critical length for design purposes in computer-aided geometric design. This paper shows an unexpected connection of critical lengths with the zeros of Bessel functions. We prove that the half of the critical length of a cycloidal space is the first positive zero of a Bessel function of the first kind.
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Partially supported by MTM2015-65433-P (MINECO/FEDER) Spanish Research Grant by Gobierno de Aragón and Fondo Social Europeo.
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Carnicer, J.M., Mainar, E. & Peña, J.M. Critical lengths of cycloidal spaces are zeros of Bessel functions. Calcolo 54, 1521–1531 (2017). https://doi.org/10.1007/s10092-017-0239-y
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DOI: https://doi.org/10.1007/s10092-017-0239-y