A new family of two-variable polynomials based on hermite polynomials

Erkus-Duman E., ÇİFTCİ H.

MATHEMATICA SLOVACA, cilt.72, sa.4, ss.885-898, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1515/ms-2022-0060
  • Dergi Adı: MATHEMATICA SLOVACA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.885-898
  • Anahtar Kelimeler: Hermite polynomials, generating function, recurrence relation, bilinear and bilateral generating functions, BERNOULLI, SYMMETRY, EULER
  • Gazi Üniversitesi Adresli: Evet

Özet

The aim of this paper is to introduce a new two-variable polynomials defined via Hermite polynomials. In order to construct some fundamental properties of these polynomials, we first derive a generating function relation. By using definition and this generating relation, we arrive at several recurrence relations, an integral representation, some implicit summation formulae, a symmetry identity for these new two-variable polynomials. Furthermore, we obtain some results which give various classes of multilinear and multilateral generating functions. Then, some special cases are presented. Finally, we also give a general class of these new polynomials and prove explicit closed-form formulae of them.