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Identities arising from higher-order Daehee polynomial bases

100%
Kim D. S., Kim T.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.
2
Content available remote

Some identities of degenerate special polynomials

100%
Kim D. S., Kim T.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper, by considering higher-order degenerate Bernoulli and Euler polynomials which were introduced by Carlitz, we investigate some properties of mixed-type of those polynomials. In particular, we give some identities of mixed-type degenerate special polynomials which are derived from the fermionic integrals on Zp and the bosonic integrals on Zp.
3
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Fully degenerate poly-Bernoulli numbers and polynomials

81%
Kim T., Kim D. S., Seo J.-J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
545-556
EN
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
4
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Fourier series of functions involving higher-order ordered Bell polynomials

81%
Kim T., Kim D. S., Jang G.-W., Jang L. C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1606-1617
EN
In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
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