Vol. 4, No. 1, 2016
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Orthogonal polynomials and Riesz bases applied to the solution of Love's equation

Pierluigi Vellucci and Alberto Maria Bersani

Vol. 4 (2016), No. 1, 55–66
DOI: 10.2140/memocs.2016.4.55
Abstract

In this paper we reinvestigate the structure of the solution of a well-known Love’s problem, related to the electrostatic field generated by two circular coaxial conducting disks, in terms of orthogonal polynomial expansions, enlightening the role of the recently introduced class of the Lucas–Lehmer polynomials. Moreover we show that the solution can be expanded more conveniently with respect to a Riesz basis obtained starting from Chebyshev polynomials.

Keywords
integral equations, numerical approximation and analysis, Love equation, Chebyshev polynomials, Lucas–Lehmer primality test, exponential bases, Riesz bases
Mathematical Subject Classification 2010
Primary: 00A69, 33C45
Milestones
Received: 15 October 2015
Revised: 8 December 2015
Accepted: 6 February 2016
Published: 11 March 2016

Communicated by Antonio Carcaterra
Authors
Pierluigi Vellucci
Dipartimento di Scienze di Base e Applicate per l’Ingegneria
Sapienza Università di Roma
Via Antonio Scarpa 16
I-00161 Rome
Italy
Alberto Maria Bersani
Dipartimento di Scienze di Base e Applicate per l’Ingegneria
Sapienza Università di Roma
Via Antonio Scarpa 16
I-00161 Rome
Italy