10.57647/cna.2025.djjh-4z18

Asymptotic Representations of Hypergeometric Bernoulli Polynomials of Order 2 Inside Regions Related to the Roots of e^w − 1 − w = 0

  1. epartment of Mathematics, Jimma University, Jimma, Ethiopia
  2. Department of Mathematics, Ambo University, Ambo, Ethiopia

Received: 2024-11-12

Revised: 2025-02-12

Accepted: 2025-12-25

Published in Issue 2025-06-30

How to Cite

Asymptotic Representations of Hypergeometric Bernoulli Polynomials of Order 2 Inside Regions Related to the Roots of e^w − 1 − w = 0. (2025). Communications in Nonlinear Analysis, 13(1), 6-15. https://doi.org/10.57647/cna.2025.djjh-4z18

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Abstract

References

  1. [1] F. T. Howard. A sequence of numbers related to the
  2. exponential function. Duke Math. J., 34:599–615,
  3. 1967.
  4. DOI:
  5. https://doi.org/10.1215/S0012-7094-67-03464-2.
  6. [2] K. H. Dilcher. Bernoulli numbers and confluent
  7. hypergeometric functions. In Number theory for the
  8. millennium, I (Urbana, IL, 2000), pages 343–363.
  9. A K Peters, Natick, MA, 2000.
  10. [3] A. Hassen and H. D. Nguyeˆn. Hypergeometric bernoulli polynomials and appell sequences. Int. J.
  11. Number Theory, 4:767–774, 2008.
  12. DOI: https://doi.org/10.1142/S1793042108001754.
  13. [4] K. H. Dilcher and L. Malloch. Arithmetic
  14. properties of bernoulli-pade numbers and ´
  15. polynomials. J. Number Theory, 92:330–347, 2002.
  16. DOI: https://doi.org/10.1006/jnth.2001.2711.
  17. [5] N. Asfaw and A. Hassen. Asymptotic behavior and
  18. zeros of hypergeometric bernoulli polynomials of order 2. JP Journal of Algebra, Number Theory
  19. and Applications, 49:51–75, 2021.
  20. [6] A. Hassen and H. D. Nguyeˆn. Hypergeometric zeta ˜
  21. functions. Int. J. Number Theory, 6:99–126, 2010.
  22. DOI: https://doi.org/10.1142/S1793042110002879.
  23. [7] R. P. Boyer and W. M. Y. Goh. On the zero
  24. attractor of the euler polynomials. Adv. in Appl.
  25. Math., 38:97–132, 2007.
  26. DOI: https://doi.org/10.1016/j.aam.2005.05.008.