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Content available remote λ-q-Sheffer sequence and its applications
Kim Taekyun, Kim Dae San, Kim Hye Kyung
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
843--865
EN
Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the view point of degenerate umbral calculus and investigate some properties related to those sequences. In addition, we give some new identities associated with q-special polynomials arising from our investigation.
2
Content available remote Some identities related to degenerate Stirling numbers of the second kind
Kim Taekyun, Kim Dae San, Kim Hye Kyung
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
812--821
EN
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.
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