On the generating functions and special functions associated with superoscillations

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Colombo F., Krausshar R., Sabadini I., ŞİMŞEK Y.

Discrete Applied Mathematics, vol.340, pp.215-227, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 340
  • Publication Date: 2023
  • Doi Number: 10.1016/j.dam.2023.07.006
  • Journal Name: Discrete Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.215-227
  • Keywords: Bernstein basis functions, Generating functions for superoscillations, Hermite polynomials, Stirling numbers, Superoscillating functions
  • Akdeniz University Affiliated: Yes

Abstract

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and many well-known families of special polynomials, numbers, and functions such as Bernstein basis functions, the Hermite polynomials, the Stirling numbers of second kind, and also the confluent hypergeometric functions. Moreover, by using generating functions, we are able to develop a recurrence relation and a derivative formula for the superoscillatory coefficients.