A Note on the q-Euler Numbers and Polynomials with Weak Weight α

We construct a new type of q-Euler numbers and polynomials with weak weight α : En,q(α), En,q(α)(x), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the q-Euler numbers En,q(α) and polynomials En,q(α)(x) with weak weight α. By means of...

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Published in:Journal of Applied Mathematics 2011-01, Vol.2011, p.1063-1076-061
Main Authors: Lee, H. Y., Jung, N. S., Ryoo, C. S.
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Language:English
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Jung, N. S.
Ryoo, C. S.
description We construct a new type of q-Euler numbers and polynomials with weak weight α : En,q(α), En,q(α)(x), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the q-Euler numbers En,q(α) and polynomials En,q(α)(x) with weak weight α. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of q-Euler polynomials En,q(α) with weak weight α.
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title A Note on the q-Euler Numbers and Polynomials with Weak Weight α
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