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

H. Y. Lee, N. S. Jung and C. S. Ryoo

Journal of Applied Mathematics, 2011, vol. 2011, 1-14

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 .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:497409

DOI: 10.1155/2011/497409

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