DOI QR코드

DOI QR Code

VARIOUS TYPES OF (p, q)-DIFFERENTIAL EQUATIONS RELATED WITH SPECIAL POLYNOMIALS

  • JUNG YOOG KANG (Department of Mathematics Education, Silla University)
  • 투고 : 2022.12.30
  • 심사 : 2023.01.06
  • 발행 : 2023.03.30

초록

We introduce several higher-order (p, q)-differential equation of which are related to (p, q)-Bernoulli polynomials. We also find some relations between (p, q)-Bernoulli, (p, q)-Euler, and (p, q)-Genocchi polynomials.

키워드

과제정보

I would like to express my gratitude to the reviewers and editors who cared about this paper.

참고문헌

  1. S. Araci, U. Duran, M. Acikgoz, H.M. Srivastava, A certain (p, q)-derivative operator and associated divided differences, J. Inequal and Appl., 301 (2016),
  2. R.B. Corcino, On (P, Q)-Binomial coefficients, Electron. J. Combin. Number Theory, 8 (2008), #A29.
  3. U. Duran, M. Acikgoz, S. Araci, On (p, q)-Bernoulli, (p, q)-Euler and (p, q)-Genocchi Polynomials, J. Comp. and Theo. Nano., November 2016.
  4. R. Jagannathan, K.S. Rao, Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series, Proceeding of the International Conference on Number Theory and Mathematical Physics, Srinivasa Ramanujan Centre, Kumbakonam, India, 20-21 December 2005.
  5. R. Jagannathan, (p, q)-Special functions, Special Functions and Differential Equations, Proceedings of a Workshop held at The Institute of Mathematical Sciences, Matras, India, January (1997), 13-24.
  6. C.S. Ryoo, J.Y. Kang, Various Types of q-Differential Equations of Higher Order for q-Euler and q-Genocchi Polynomials, Mathematics 10 (2022), 1-16.
  7. N. Saba and A. Boussayoud, New Theorem on Symmetric Functions and Their Applications on Some (p, q)-numbers, Journal of Applied Mathematics and Informatics, 40 (2022), 243-258. https://doi.org/10.14317/JAMI.2022.243
  8. P.N. Sadjang, On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas, arXiv:1309.3934 [math.QA] (2013).
  9. M. Wachs, D. White, (p, q)-Stirling numbers and set partition statistics, J. Conbin. Theory, A 56 (1991), 27-46.  https://doi.org/10.1016/0097-3165(91)90020-H