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A Note on the ð ‘ž -Euler Numbers and Polynomials with Weak Weight ð ›¼

Author

Listed:
  • H. Y. Lee
  • N. S. Jung
  • C. S. Ryoo

Abstract

We construct a new type of ð ‘ž -Euler numbers and polynomials with weak weight ð ›¼ : ð ¸ ( ð ›¼ ) ð ‘› , ð ‘ž , ð ¸ ( ð ›¼ ) ð ‘› , ð ‘ž ( ð ‘¥ ) , respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the ð ‘ž -Euler numbers ð ¸ ( ð ›¼ ) ð ‘› , ð ‘ž and polynomials ð ¸ ( ð ›¼ ) ð ‘› , ð ‘ž ( ð ‘¥ ) with weak weight ð ›¼ . By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of ð ‘ž -Euler polynomials ð ¸ ( ð ›¼ ) ð ‘› , ð ‘ž with weak weight ð ›¼ .

Suggested Citation

  • H. Y. Lee & N. S. Jung & C. S. Ryoo, 2011. "A Note on the ð ‘ž -Euler Numbers and Polynomials with Weak Weight ð ›¼," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-14, November.
    • Handle: RePEc:hin:jnljam:497409
    DOI: 10.1155/2011/497409
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    Cited by:

    1. Dae San Kim & Taekyun Kim, 2012. "Bernoulli Basis and the Product of Several Bernoulli Polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-12, September.

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