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1
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.
3
Content available remote On some summation formulas
Kim Taekyun, Kim Dae San, Lee Hyunseok, Kwon Jongkyum
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
1--7
EN
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals.
4
Content available remote Fully degenerate Bernoulli numbers and polynomials
Kim Taekyun, Kim Dae San, Park Jin-Woo
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
604--614
EN
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.
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