q-Generalized Euler numbers and polynomials

By Taekyun Kim. 2006

78 citations recorded by the source corpus.

Recently, B. A. Kupershmidt constructed reflection symmetries of q-Bernoulli polynomials (see [12]). In this paper, we study new q-extensions of Euler numbers and polynomials by using the method of Kupershmidt. We also investigate the properties of symmetries of these q-Euler polynomials by using q-derivatives and q-integrals.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/9f4e8153d35899e36685ff473f107ddb9403453b

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In Algebra and Number Theory

In Applied Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

Note on the Euler Numbers and Polynomials (2008, background): “n=0 En t n! , for |t| ≤ π, (see [1-31]), are known as the Euler numbers.”
Identities involving Frobenius–Euler polynomials arising from non-linear differential equations (2012, background): “In the special case, x = 0, H (r) n (0 | u) = H (r) n (u) are called the n-th Frobenius-Euler numbers of order r (see [1-15]).”
q-Extensions of Some Relationships Between the Bernoulli and Euler Polynomials (2011, background): “([16-22] and [23]), Ozden and Simsek [26], Ryoo et al.”
Some Approximation Properties of -Baskakov-Beta-Stancu Type Operators (2013, unknown): “The q-Jackson integrals and the q-improper integrals are defined as [12, 13]”
Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, unknown): “( [26], [27], [28], [29], [31], [32], [33], [34], [36] and [37]), Luo and Srivastava [54], Ozden and Simsek [57], Ryoo et al.”