Shortened recurrence relations for generalized Bernoulli numbers and polynomials
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DOI: 10.1016/j.jnt.2016.12.014
Abstract: Abstract It is the main purpose of this paper to study shortened recurrence relations for generalized Bernoulli numbers and polynomials attached to χ, χ being a primitive Dirichlet character, in which some of the preceding… read more here.
Keywords: bernoulli numbers; numbers polynomials; recurrence relations; relations generalized ... See more keywords
Divisibility properties of the r-Bell numbers and polynomials
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DOI: 10.1016/j.jnt.2017.01.022
Abstract: In the present article we extend several arithmetical results to a family of generalized Bell numbers called r-Bell numbers. In particular, we generalize some congruences such as Touchard's congruence, Sun–Zagier congruence for Bell and derangement… read more here.
Keywords: properties bell; divisibility properties; bell numbers; numbers polynomials ... See more keywords
On (ρ,q)-Euler numbers and polynomials associated with (ρ,q)-Volkenborn integrals
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DOI: 10.1142/s179304211850015x
Abstract: Recently, Araci et al. introduced (ρ,q)-analogue of the Haar distribution and by means of the distribution, they constructed (ρ,q)-Volkenborn integral yielding to Carlitz’s-type (ρ,q)-Bernoulli numbers and polynomials. The aim of the present paper is to… read more here.
Keywords: numbers polynomials; volkenborn integrals; polynomials associated; associated volkenborn ... See more keywords
A note on degenerate multi-poly-Bernoulli numbers and polynomials
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DOI: 10.2298/aadm200510005k
Abstract: In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate some properties for those… read more here.
Keywords: numbers polynomials; degenerate multi; poly bernoulli; multi poly ... See more keywords
On fully degenerate Bell numbers and polynomials
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DOI: 10.2298/fil2002507d
Abstract: Recently, the partially degenerate Bell numbers and polynomials were introduced as a degenerate version of Bell numbers and polynomials. In this paper, as a further degeneration of them, we study fully degenerate Bell numbers and… read more here.
Keywords: degenerate bell; fully degenerate; bell numbers; numbers polynomials ... See more keywords
Identities and relations for special numbers and polynomials: An approach to trigonometric functions
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DOI: 10.2298/fil2002535k
Abstract: In this paper, by using trigonometric functions and generating functions, identities and relations associated with special numbers and polynomials are derived. Relations among the combinatorial numbers, the Bernoulli polynomials, the Euler numbers, the Stirling numbers… read more here.
Keywords: special numbers; numbers polynomials; identities relations; trigonometric functions ... See more keywords
Some new identities and formulas for higher-order combinatorial-type numbers and polynomials
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DOI: 10.2298/fil2002551k
Abstract: The main purpose of this paper is to provide various identities and formulas for higherorder combinatorial-type numbers and polynomials with the help of generating functions and their both functional equations and derivative formulas. The results… read more here.
Keywords: numbers polynomials; combinatorial type; type numbers; identities formulas ... See more keywords
On poly-Bell numbers and polynomials
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DOI: 10.2989/16073606.2020.1805039
Abstract: Abstract This paper aims to construct a new family of numbers and polynomials which are related to the Bell numbers and polynomials by means of the confluent hypergeometric function. We give various properties of these… read more here.
Keywords: numbers polynomials; bell numbers; poly bell; bell ... See more keywords
Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials
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DOI: 10.3390/sym11070847
Abstract: In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p-adic invariant integrals on Z p . In particular, we derive various… read more here.
Keywords: numbers polynomials; bernoulli numbers; identities ordinary; degenerate bernoulli ... See more keywords