Chapman & Hall/CRC eBooks

Quantum wavelets

Sabrine Arfaoui, Anouar Ben Mabrouk, Carlo Cattani

Published Apr 12, 2021• 0 citations

Abstract

Quantum wavelets are special types of wavelet functions characterized by special properties that may not be satisfied by other functions. This chapter aims to develop wavelet functions based on some special functions such as Bessel one. Bessel functions form an important class of special functions and are applied almost everywhere in mathematical physics. There are three main ways to introduce Bessel functions. The first one is due to a special type of second-order singular and linear differential equations where the Bessel functions form a generator set of solutions. The second one resembles orthogonal polynomials and provides Bessel functions as solutions of three-level recurrent singular and linear functional equation. The third one provides Bessel functions via the Rodriguez derivation formula.

DOI: 10.1201/9781003096924-5

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