Multivariate Interpolation Functions of Higher-Order -Euler Numbers and Their Applications

By Hacer Ozden, I. N. Cangul, Yilmaz Simsek. 2008

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The aim of this paper, firstly, is to construct generating functions of 𝑞-Euler numbers and polynomials of higher order by applying the fermionic 𝑝-adic 𝑞-Volkenborn integral, secondly, to define multivariate 𝑞-Euler zeta function (Barnes-type Hurwitz 𝑞-Euler zeta function) and 𝑙-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz 𝑞-Euler zeta function and multivariate 𝑞-Euler 𝑙-function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/42730bafaac84209ac8514f00ff030f223115b13

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Some families of Genocchi type polynomials and their interpolation functions (2012, methodology): “ = e into Theorem 11, then we have mX−1 k=0 (−1)kkn = Gn(1,e) −(−1)mGn(m;1,e,e) 2n = Gn −(−1)mGn(m) 2n . Thus, by (3), Theorem 11 reduces to mX−1 k=0 (−1)kkn = En −(−1)mEn(m) 2 , cf. ([4], [5], [14], [22], [20], [19], [28]). 4 Interpolation Functions In this section, we construct interpolation funct”
Identities involving Frobenius–Euler polynomials arising from non-linear differential equations (2012, methodology): “ −u | {z } r− times ext = X∞ n=0 H(r) n (x | u) tn n! for u ∈ Cwith u 6= 1 . (6) 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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]). In this paper we derive non-linear diﬀerential ”