SOME RELATIONS ON HERMITE-HERMITE MATRIX POLYNOMIALS


Shehata A., ÇEKİM B.

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, vol.78, no.1, pp.181-194, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 78 Issue: 1
  • Publication Date: 2016
  • Journal Name: UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.181-194
  • Keywords: Matrix functions, Chebyshev-Chebyshev, Legendre-Legendre, Hermite-Hermite, Chebyshev-Hermite, Legendre-Hermite matrix, polynomials, Matrix differential equation
  • Gazi University Affiliated: Yes

Abstract

The main purpose of this paper is to define a new extension of Hermite-Hermite matrix polynomials (HHMP) and derive some properties such as recurrence relations and matrix differential equation for generalized Hermite-Hermite matrix polynomials. We derive addition and multiplication theorem, and summation formula for generalized HHMP. Furthermore, via integral transform, the new families of Chebyshev-Chebyshev, Legendre-Legendre, Chebyshev-Hermite and Legendre-Hermite matrix polynomials are introduced, from which a variety of interesting results follows as special cases.