• Journal of Applied and Pure Mathematics
• /
• 제6권1_2호
• /
• pp.47-54
• /
• 2024

In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.

• 대한수학회보
• /
• 제58권6호
• /
• pp.1463-1481
• /
• 2021

Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.

• Journal of applied mathematics & informatics
• /
• 제36권1_2호
• /
• pp.29-38
• /
• 2018

In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

• 대한수학회보
• /
• 제55권6호
• /
• pp.1909-1920
• /
• 2018

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

• Journal of applied mathematics & informatics
• /
• 제38권5_6호
• /
• pp.601-609
• /
• 2020

In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

• 대한수학회보
• /
• 제56권2호
• /
• pp.491-499
• /
• 2019

The problem of finding fast computing methods for Bernoulli numbers has a long and interesting history. In this paper, the author provides new proofs for two lacunary recurrence relations with gaps of length four and eight for the Bernoulli numbers. These proofs invoked the fact that the nth powers of ${\pi}^2$, ${\pi}^4$ and ${\pi}^8$ can be expressed in terms of the nth elementary symmetric functions.

• 호남수학학술지
• /
• 제41권1호
• /
• pp.117-133
• /
• 2019

In the current investigation, we obtain the generating function for Hermite-based degenerate Bernoulli polynomials attached to ${\chi}$ of higher order using p-adic methods over the ring of integers. Useful identities, formulae and relations with well known families of polynomials and numbers including the Bernoulli numbers, Daehee numbers and the Stirling numbers are established. We also give identities of symmetry and additive property for Hermite-based generalized degenerate Bernoulli polynomials attached to ${\chi}$ of higher order. Results are supported by remarks and corollaries.

• 대한수학회논문집
• /
• 제36권1호
• /
• pp.19-26
• /
• 2021

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.

• Journal of applied mathematics & informatics
• /
• 제23권1_2호
• /
• pp.205-214
• /
• 2007

Over the years, there has been increasing interest in solving mathematical problems with the aid of computers. The main purpose of this paper is to investigate the roots of the q-Bernoulli polynomials $B_{n,q}{^r}(x)$ for values of the index n by using computer. Finally, we consider the reflection symmetries of the q-Bernoulli polynomials $B_{n,q}{^r}(x)$.

• 대한수학회보
• /
• 제42권3호
• /
• pp.617-622
• /
• 2005

In this paper, using Gauss multiplication formula, a recurrence relation for Bernoulli numbers, generalizing Namias' results, is given.