A B-spline approach to q-Eulerian polynomials

Dişibüyük Ç., Ulutas S.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.366, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 366
  • Publication Date: 2020
  • Doi Number: 10.1016/j.cam.2019.112427
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: q-Eulerian numbers, q-Eulerian polynomials, q-Euler-Frobenius polynomials, q-exponential spline, q-exponential Euler polynomials, Worpitzky identity
  • Dokuz Eylül University Affiliated: Yes

Abstract

We present q-analogues of exponential Euler polynomials and Euler-Frobenius polynomials from B-splines with knots both at q-integers and in geometric progression. We also investigate the relations between q-Eulerian numbers, q-Eulerian polynomials, q-Euler-Frobenius polynomials and B-splines. We derive q-Euler-Frobenius polynomials using q-analogue of exponential splines. It is shown that B-splines with knots at q-integers and B-splines with knots in geometric progression have same values on their knot points. We also construct a q-analogue of Worpitzky identity. (C) 2019 Elsevier B.V. All rights reserved.