Finite bivariate biorthogonal I - Konhauser polynomials

Güldoğan Lekesi̇z E., ÇEKİM B., Özarslan M. A.

Journal of Computational and Applied Mathematics, vol.476, 2026 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 476
  • Publication Date: 2026
  • Doi Number: 10.1016/j.cam.2025.117106
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Keywords: Finite biorthogonal polynomial, Fourier transform, Fractional operator, Konhauser polynomial, Laplace transform, Mittag-Leffler function
  • Gazi University Affiliated: Yes

Abstract

In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval's identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.