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Fourier series of higher-order Bernoulli functions and their applications

In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them. MSC: 11B68, 42A16.

Some identities of Korobov-type polynomials associated with p-adic integrals on Z p

In this paper, we consider Korobov-type polynomials derived from the bosonic and fermionic p-adic integrals on Z p , and we give some interesting and new identities of those polynomials and of their mixed-types. MSC: 11B68, 11B83, 11S80, 05A19.

A note on degenerate poly-Bernoulli numbers and polynomials

In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind. MSC: 11B68, 11B73, 11B83.

Korobov polynomials of the third kind and of the fourth kind

The first degenerate version of the Bernoulli polynomials of the second kind appeared in the paper by Korobov (Math Notes 2:77–19, 1996; Proceedings of the IV international conference modern problems of number theory and its applications, pp 40–49, 2001). In this paper, we study two degenerate versions of the Bernoulli polynomials of the second kind which will be called Korobov ...

Some identities of Laguerre polynomials arising from differential equations

In this paper, we derive a family of ordinary differential equations from the generating function of the Laguerre polynomials. Then these differential equations are used in order to obtain some properties and new identities for those polynomials. MSC: 05A19, 33C45, 11B37, 35G35.

Degenerate poly-Cauchy polynomials with a q parameter

In this paper, the degenerate poly-Cauchy polynomials with a q parameter of the first and the second kind are introduced and their properties are studied. For these polynomials, some explicit formulas, recurrence relations, and connections with a few previously known families of polynomials are established. MSC: 05A19, 05A40, 11B83.

Linear differential equations for families of polynomials

In this paper, we present linear differential equations for the generating functions of the Poisson-Charlier, actuarial, and Meixner polynomials. Also, we give an application for each case.

Powers under umbral composition and degeneration for Sheffer sequences

In this paper we study the powers under umbral composition and degeneration for Sheffer sequences, where we presented several applications related to Bernoulli polynomials, Frobenius-Euler polynomials, falling factorial polynomials and Bell polynomials and their degeneration cases. MSC: 05A19, 05A40, 11B83.

Degenerate q-Euler polynomials

Recently, some identities of degenerate Euler polynomials arising from p-adic fermionic integrals on Z p were introduced in Kim and Kim (Integral Transforms Spec. Funct. 26(4):295-302, 2015). In this paper, we study degenerate q-Euler polynomials which are derived from p-adic q-integrals on Z p . MSC: 11B68, 11S80.

Barnes-type Narumi polynomials

In this paper, we study the Barnes-type Narumi polynomials with umbral calculus viewpoint. From our study, we derive various identities of the Barnes-type Narumi polynomials.MSC: 05A19, 05A40, 11B68.

On q-analogs of degenerate Bernoulli polynomials

The degenerate Bernoulli polynomials were introduced by Carlitz and rediscovered later by Ustiniv under the name of Korobov polynomials of the second kind (see Carlitz in Arch. Math. (Basel) 7:28-33, 1956; Util. Math. 15:51-88, 1979). In this paper, we study q-analogs of degenerate Bernoulli polynomials and give some formulas related to these polynomials. MSC: 05A19, 05A30, 11B68, ...

Three variable symmetric identities involving Carlitz-type \(q\) -Euler polynomials

In this paper, we derive several identities of symmetry in three variables related to Carlitz-type \(q\)-Euler polynomials and alternating \(q\)-power sums. These and most of their identities are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the fermionic \(p\)-adic \(q\)-integral expressions of the ...

Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials

In this paper, we introduce the mixed-type polynomials: Barnes-type Daehee polynomials of the second kind and poly-Cauchy polynomials of the second kind. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.MSC: 05A19, 05A40, 11B68, 11B75.

Some properties of higher-order Daehee polynomials of the second kind arising from umbral calculus

In this paper, we study the higher-order Daehee polynomials of the second kind from the umbral calculus viewpoint and give various identities of the higher-order Daehee polynomials of the second kind arising from umbral calculus.

Poly-Cauchy and Peters mixed-type polynomials

The Peters polynomials are a generalization of Boole polynomials. In this paper, we consider Peters and poly-Cauchy mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities of those polynomials associated with special polynomials.

Poly-Cauchy numbers and polynomials of the second kind with umbral calculus viewpoint

Dae San Kim 1 Taekyun Kim 0 0 Department of Mathematics, Kwangwoon University , Seoul, 139-701 , Republic of Korea 1 Department of Mathematics, Sogang University , Seoul, 121-742 , Republic of Korea

Poly-Cauchy and Peters mixed-type polynomials

The Peters polynomials are a generalization of Boole polynomials. In this paper, we consider Peters and poly-Cauchy mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities of those polynomials associated with special polynomials.

Some identities of q-Euler polynomials arising from q-umbral calculus

Recently, Araci-Acikgoz-Sen derived some interesting identities on weighted q-Euler polynomials and higher-order q-Euler polynomials from the applications of umbral calculus (see (Araci et al. in J. Number Theory 133(10):3348-3361, 2013)). In this paper, we develop the new method of q-umbral calculus due to Roman, and we study a new q-extension of Euler numbers and polynomials ...

Degenerate poly-Bernoulli polynomials with umbral calculus viewpoint

In this paper, we consider the degenerate poly-Bernoulli 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. MSC: 05A19, 05A40, 11B83.

Hermite and poly-Bernoulli mixed-type polynomials

In this paper, we consider Hermite and poly-Bernoulli mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities associated with Stirling numbers, Bernoulli and Frobenius-Euler polynomials of higher order.