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Some identities related to degenerate Stirling numbers of the second kind

Kim Taekyun, Kim Dae San, Kim Hye Kyung

Demonstratio Mathematica

2022

Vol. 55, nr 1

812--821

The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and polynomials. The aim of this article is to further study some identities and properties related to the degenerate Stirling numbers of the second kind, in connection with the degenerate Bell polynomials, the degenerate Fubini polynomials, the degenerate Bernoulli polynomials, and the degenerate Euler polynomials.

Fully degenerate Bernoulli numbers and polynomials

Kim Taekyun, Kim Dae San, Park Jin-Woo

Demonstratio Mathematica

2022

Vol. 55, nr 1

604--614

The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp . We find some explicit expressions for the fully degenerate Bernoulli polynomials and numbers in terms of the degenerate Stirling numbers of the second kind, the degenerate r -Stirling numbers of the second kind, and the degenerate Stirling polynomials. We also consider the degenerate poly-Bernoulli polynomials and derive explicit representations for them in terms of the same degenerate Stirling numbers and polynomials.

Generalized binomial convolution of the mth powers of the consecutive integers with the general Fibonacci sequence

Kılıç E., Akkus I., Ömür N., Ulutaş Y.

Demonstratio Mathematica

2016

Vol. 49, nr 4

379--385

In this paper, we consider Gauthier’s generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.