On the multiple q-Genocchi and Euler numbers

By Taekyun Kim. 2008

109 citations recorded by the source corpus.

The purpose of this paper is to present a systematic study of some families of multiple q-Genocchi and Euler numbers by using the multivariate q-Volkenborn integral (= p-adic q-integral) on ℤp. The investigation of these q-Genocchi numbers and polynomials of higher order leads to interesting identities related to these objects. The results of the present paper cover earlier results concerning ordinary q-Genocchi numbers and polynomials.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/13e1fc3e5ccf02b41cbea6f6ccbddc7898c5c5d9

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler (2011, background): “On the subject of the Genocchi polynomials Gn(x) and their various extensions, a remarkably large number of investigations have appeared in the literature (see, for example, [9], [12], [21], [22], [23], [25], [28], [30], [34], [38], [39], [40], [43], [41] [48], [49], [50], [58] and [80]; see also th”
Some families of Genocchi type polynomials and their interpolation functions (2012, background): “cchi numbers, Euler numbers and Bernoulli numbers are given by: En = Gn+1 n+1 , (3) G 2n = 2(1−2 2n)B 2n = 2nE 2n−1(0), where Bn and En are Bernoulli numbers and Euler Numbers respectively, cf. ([4], [11], [14], [7], [16], [13], [24], [28], [26]). The ordinary Genocchi Polynomials are deﬁned by mean”
A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials (2012, unknown): “2) I−1 (f1) + I−1 (f) = 2f (0) here f1 (x) := f (x+ 1) (for details, see[3-24]).”