Roberto B. Corcino

Asymptotic Estimates for r-Whitney Numbers of the Second Kind

The r-Whitney numbers of the second kind are a generalization of all the Stirling-type numbers of the second kind which are in line with the unified generalization of Hsu and Shuie. In this paper, asymptotic formulas for r-Whitney numbers of the second kind with integer and real parameters are obtained and the range of validity of each formula is established.

Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters

In this paper we investigate special generalized Bernoulli polynomials with a,b,c parameters that generalize classical Bernoulli numbers and polynomials. The present paper deals with some recurrence formulae for the generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters. Poly-Bernoulli numbers satisfy certain recurrence relationships which are used in many computations involving poly-Bernoulli numbers. Obtaining a closed formula for generalization of poly-Bernoulli numbers with a,b,c paramerers therefore seems to be a natural and important problem. By using the generalization of poly-Bernoulli polynomials with a,b,c parameters of negative index we define symmetrized generalization of poly-Bernoulli polynomials with a,b parameters of two variables and we prove duality property for them. Also by stirling numbers of the second kind we will find a closed formula for them. Furthermore we generalize the Arakawa-Kaneko Zeta functions and by using the Laplace-Mellin integral, we define generalization of Arakawa-Kaneko Zeta functions with a,b parameters and we obtain an interpolation formula for the generalization of poly-Bernoulli numbers and polynomials with a,b parameters. Furthermore we present a link between this type of Zeta functions and Dirichlet series. By our interpolation formula, we will interpolate the generalization of Arakawa-Kaneko Zeta functions with a,b parameters.

On Generalized Bell Polynomials

It is shown that the sequence of the generalized Bell polynomials Sn(x) is convex under some restrictions of the parameters involved. A kind of recurrence relation for Sn(x) is established, and some numbers related to the generalized Bell numbers and their properties are investigated.

An Asymptotic Formula for -Bell Numbers with Real Arguments

The -Bell numbers are generalized using the concept of the Hankel contour. Some properties parallel to those of the ordinary Bell numbers are established. Moreover, an asymptotic approximation for -Bell numbers with real arguments is obtained.

More properties on multi-poly-Euler polynomials

In this paper, we establish more properties of generalized poly-Euler polynomials with three parameters and we investigate a kind of symmetrized generalization of poly-Euler polynomials. Moreover, we introduce a more general form of multi-poly-Euler polynomials and obtain some identities parallel to those of the generalized poly-Euler polynomials.

The estimation of the zeros of the Bell and r-Bell polynomials

It is a classical result that the zeros of the Bell polynomials are real and negative. In this study we deal with the asymptotic growth of the leftmost zeros of the Bell polynomials and generalize the results for the r-Bell polynomials, too. In addition, we offer a heuristic approach for the approximation of the maximizing index of the Stirling numbers of both kind.

Asymptotic Estimates for Second Kind Generalized Stirling Numbers

Asymptotic formulas for the generalized Stirling numbers of the second kind with integer and real parameters are obtained and ranges of validity of the formulas are established. The generalizations of Stirling numbers considered here are generalizations along the line of Hsu and Shuies unified generalization.

Equivalent asymptotic formulas of second kind r-Whitney numbers

Asymptotic formulas of the second kind r-Whitney numbers for positive real parameters are obtained using a modified saddle-point method and by another analytic method. Moreover, the formulas obtained are shown to be asymptotically equivalent in the range of a parameter where they are both valid.

A q-Analogue of Rucinski-Voigt Numbers

A -analogue of Rucinski-Voigt numbers is defined by means of a recurrence relation, and some properties including the orthogonality and inverse relations with the -analogue of the limit of the differences of the generalized factorial are obtained.

Integrals and derivatives connected to the r-Lambert function

ABSTRACT In this paper, we derive some formulas for higher order derivatives of r-Lambert functions. Moreover, an integration formula involving powers of r-Lambert function is obtained.