Orthogonalizing q-Bernoulli polynomials

Kus S., TUĞLU N.

Demonstratio Mathematica, cilt.58, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/dema-2025-0133
  • Dergi Adı: Demonstratio Mathematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: block-pulse functions, orthonormal polynomials, q-Bernoulli polynomials
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OB n (x, q) {{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials. We demonstrate the relationship between polynomials OB n (x, q) {{\rm{OB}}}_{n}(x,q) and the little q-Legendre polynomials, and derive a generalized formula for OB n (x, q) {{\rm{OB}}}_{n}(x,q) by leveraging the little q-Legendre polynomials. Furthermore, we present some properties of polynomials OB n (x, q) {{\rm{OB}}}_{n}(x,q). Finally, we introduce a hybrid of block-pulse function and orthogonal polynomials OB n (x, q) {{\rm{OB}}}_{n}(x,q) and examine various properties of these polynomials.