SOME RELATIONS ON HERMITE-HERMITE MATRIX POLYNOMIALS

Shehata A., ÇEKİM B.

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, cilt.78, sa.1, ss.181-194, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 78 Sayı: 1
  • Basım Tarihi: 2016
  • Dergi Adı: UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.181-194
  • Anahtar Kelimeler: Matrix functions, Chebyshev-Chebyshev, Legendre-Legendre, Hermite-Hermite, Chebyshev-Hermite, Legendre-Hermite matrix, polynomials, Matrix differential equation
  • Gazi Üniversitesi Adresli: Evet

Özet

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.