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On multiple interpolation functions of the Nörlund-type \(q\)-Euler polynomials. (English) Zbl 1194.11027

Summary: In [Russ. J. Math. Phys. 13, No. 3, 293–298 (2006; Zbl 1163.11311) and Adv. Stud. Contemp. Math., Kyungshang 18, No. 2, 105–112 (2009; Zbl 1213.11049)], T. Kim defined new generating functions of the Genocchi, Nörlund-type \(q\)-Euler polynomials and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type \(q\)-zeta function. This function interpolates Nörlund-type \(q\)-Euler polynomials at negative integers. We also give some identities related to these polynomials and functions. Furthermore, we give some remarks about approximations of Bernoulli and Euler polynomials.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
05A15 Exact enumeration problems, generating functions
11B65 Binomial coefficients; factorials; \(q\)-identities
05A30 \(q\)-calculus and related topics
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References:

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