Cristina 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.

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.

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.

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.

The Peak of Noncentral Stirling Numbers of the First Kind

We locate the peak of the distribution of noncentral Stirling numbers of the first kind by determining the value of the index corresponding to the maximum value of the distribution.

The Hankel Transform of -Noncentral Bell Numbers

We define two forms of -analogue of noncentral Stirling numbers of the second kind and obtain some properties parallel to those of noncentral Stirling numbers. Certain combinatorial interpretation is given for the second form of the -analogue in the context of 0-1 tableaux which, consequently, yields certain additive identity and some convolution-type formulas. Finally, a -analogue of noncentral Bell numbers is defined and its Hankel transform is established.