DOI QR코드

DOI QR Code

A STUDY ON DEGENERATE (p, q, h)-BERNOULLI POLYNOMIALS AND NUMBERS

  • HUI YOUNG LEE (Department of Mathematics, Hannam University)
  • 투고 : 2024.04.23
  • 심사 : 2024.08.07
  • 발행 : 2024.09.30

초록

This paper introduces a more generalized form of the degenerated q-Bernoulli polynomial, termed (p,q)-Bernoulli polynomial, and presents their properties. Various properties including symmetry were investigated, yet properties of symmetry were not identified. However, in the process, another property was discovered, and the purpose is to introduce this newly found property.

키워드

과제정보

This work was supported by the research grant of the Hannam University.

참고문헌

  1. L. Carlitz, A degenerated Staudt-Clausen theorem, Arch. Math. 7 (1956), 28-33. 
  2. L. Carlitz, Degenerated Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15 (1979), 51-88. 
  3. C.S. Ryoo, Some properties of degenerate carlitz-type twisted q-euler numbers and polynomials, J. Appl. Math & Informatics 39 (2021), 1-11. 
  4. C.S. Ryoo, Some properties of poly-cosine tangent and poly-sine tangent polynomials, J. Appl. Math & Informatics 40 (2022), 371-391. 
  5. N.S. Jung, C.S. Ryoo, A research on linear (p,q)-difference equations of higher order, J. Appl. Math & Informatics 41 (2023), 167-179. 
  6. C.S. Ryoo, Distribution of the roots of the second kind Bernoulli polynomials, J. Comput. Anal. Appl. 13 (2011), 971-976. 
  7. C.S. Ryoo, Numerical investigation of zeros of the fully modified (p, q)-poly-Euler polynomials, Journal of Computational Analysis and Applications 32 (2024), 276-285. 
  8. Hui Young Lee, Chung Hyun Yu, A study on degenerate q-Bernoulli polynomials and numbers, J. Appl. Math. & Informatics 41 (2023), 1303-1315. 
  9. J.Y. Kang, C.S. Ryoo, Approximate Roots and Properties of Differential Equations for Degenerate q-Special Polynomials, Mathematics 11 (2023), 2803. 
  10. P.T. Young, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, Journal of Number Theory 128 (2008), 738-758. 
  11. Yilmaz Simsek, Twisted (h, q)-Bernoulli numbers and polynomials related to twisted (h, q)-zeta function and L-function, Journal of Mathematical Analysis & Applications 324 (2006), 790-804. 
  12. H.Y. Lee, Y.R. Kim, On the second kind degenerated Bernoulli polynomials and numbers and their applications, Far East Journal of Mathemaical Sciences 102 (2017), 793-809. 
  13. H.Y. Lee, A note of the modified Bernoulli polynomials and it's the location of the roots, J. Appl. Math & Informatics 38 (2020), 291-300.