32 papers found.

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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.

Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from ...

In this paper, we investigate some identities of q-extensions of special polynomials which are derived from the fermonic q-integral on Zp and the bosonic q-integral on Zp.

We consider the Witt-type formula for the nth twisted Daehee numbers and polynomials and investigate some properties of those numbers and polynomials. In particular, the nth twisted Daehee numbers are closely related to higher-order Bernoulli numbers and Bernoulli numbers of the second kind.

In this paper, we derive some interesting identities involving Gegenbauer polynomials arising from the orthogonality of Gegenbauer polynomials for the inner product space P n with respect to the weighted inner product 〈 p 1 , p 2 〉 = ∫ − 1 1 p 1 ( x ) p 2 ( x ) ( 1 − x 2 ) λ − 1 2 d x .

In this paper, by using the orthogonality type as defined in the umbral calculus, we derive an explicit formula for several well-known polynomials as a linear combination of the Apostol-Euler polynomials.MSC: 05A40.

The purpose of this paper is to investigate some interesting identities on the Bernoulli and Euler polynomials arising from the orthogonality of Legendre polynomials in the inner product space P n .

In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus to have alternative ways.MSC: 05A10, 05A19.

In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials.MSC: 05A40, 05A19.

In (Kim and Kim in J. Inequal. Appl. 2013:111, 2013; Kim and Kim in Integral Transforms Spec. Funct., 2013, doi:10.1080/10652469.2012.754756), we have investigated some properties of higher-order Bernoulli and Euler polynomial bases in P n = { p ( x ) ∈ Q [ x ] | deg p ( x ) ≤ n } . In this paper, we derive some interesting identities of higher-order Bernoulli and Euler polynomials ...

Abstract In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials. Finally, we give some interesting and new identities of several special polynomials arising from umbral calculus. MSC: 05A10, 05A19.

In this paper, we investigate some properties of polynomials related to Sheffer sequences. Finally, we derive some identities of higher-order Frobenius-Euler polynomials.

In this paper, we derive some identities of Bernoulli, Euler, and Abel polynomials arising from umbral calculus.MSC: 05A10, 05A19.

In this paper, we study some p-adic Frobenius-Euler measure related to umbral calculus in the p-adic case. Finally, we derive some identities of Frobenius-Euler polynomials from our study.MSC: 05A10, 05A19.

In this paper, we derive some interesting identities on Bernoulli and Euler polynomials by using the orthogonal property of Laguerre polynomials.

In this paper, we derive some interesting identities involving Gegenbauer polynomials arising from the orthogonality of Gegenbauer polynomials for the inner product space P n with respect to the weighted inner product 〈 p 1 , p 2 〉 = ∫ − 1 1 p 1 ( x ) p 2 ( x ) ( 1 − x 2 ) λ − 1 2 d x .

In this paper, we derive some interesting identities on Bernoulli and Euler polynomials by using the orthogonal property of Laguerre polynomials.

In this paper, we construct a new q-extension of Euler numbers and polynomials with weight related to fermionic p-adic q-integral on Zp and give new explicit formulas related to these numbers and polynomials.

In this paper, we investigate some properties of polynomials related to Sheffer sequences. Finally, we derive some identities of higher-order Frobenius-Euler polynomials.

In this paper, we derive the identities of higher-order Bernoulli, Euler and Frobenius-Euler polynomials from the orthogonality of Hermite polynomials. Finally, we give some interesting and new identities of several special polynomials arising from umbral calculus. MSC: 05A10, 05A19.