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In this paper, we consider the problem of representing any polynomial in terms of the degenerate Daehee polynomials and more generally of the higher-order degenerate Daehee polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples.

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.

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.

In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression of the degenerate hyperharmonic numbers in terms of the degenerate harmonic numbers. This is a degenerate version of the corresponding identity representing the hyperharmonic numbers in terms of harmonic numbers due to Conway and Guy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to represent any polynomial in terms of degenerate Frobenius–Euler polynomials and, more generally, of higher-order degenerate Frobenius–Euler polynomials. Explicit formulas with the help of umbral calculus are derived and the obtained results are illustrated by some examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing them to central factorials and central Bell polynomials of the second kind respectively when k = 1 . We also show some relations: between poly-central factorial sequences and power of x; between poly-central Bell polynomials and power of x; between poly-central Bell polynomials and the poly-Bell polynomials; between poly-central Bell polynomials and higher order type 2 Bernoulli polynomials of second kind; recurrence formula of poly-central Bell polynomials. [ABSTRACT FROM AUTHOR]

We present several explicit formulas and recurrence relations for the degenerate Mittag-Leffler polynomials. We also give several connections between Mittag-Leffler polynomials and other known families of polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we consider Korobov-type polynomials derived from the bosonic and fermionic p-adic integrals on $\mathbb{Z}_{p}$, and we give some interesting and new identities of those polynomials and of their mixed-types. [ABSTRACT FROM AUTHOR]

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers. [ABSTRACT FROM AUTHOR]

In this paper, we study several properties for the degenerate poly-Cauchy polynomials. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials. [ABSTRACT FROM AUTHOR]