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Roberto B. Corcino

Publications and source records attributed to Roberto B. Corcino.

At least 19 recordsLinked to original sources
arXiv2026

Degenerate Hurwitz-Lerch Type Families of Poly-Bernoulli and Poly-Cauchy Numbers with Parameters $(α,a)

In this paper, we introduce degenerate Hurwitz-Lerch type families of poly-Bernoulli and poly-Cauchy numbers with parameters $(α,a)$. These families are defined by means of degenerate Hurwitz-Lerch type zeta functions and their factorial analogues. We establish the generating functions of these numbers and derive explicit formulas in terms of the degenerate Stirling numbers of the first and second kinds. In particular, we obtain closed-form expressions for the degenerate two-parameter Hurwitz-Lerch type poly-Bernoulli numbers and for the corresponding poly-Cauchy numbers of the first and second kinds. These results extend several known identities for classical and generalized poly-Bernoulli and poly-Cauchy numbers.

math.CO↗
arXiv2026

The Multivariable Generalized Hermite-Type-Genocchi Polynomials of Order a

This study presents a new class of poly-Genocchi polynomials constructed through the integration of some interesting polynomials. The resulting family, referred to as the multivariable generalized Hermite-type-Genocchi polynomials of order a, is investigated in detail. Several fundamental properties are derived, including explicit representations, addition formulas, and polynomial expansions. In addition, relationships between this new family of polynomials and a certain generalized Stirling numbers of the first kind are established.

math.CO↗
arXiv2021

Translated Logarithmic Lambert Function and its Applications to Three-Parameter Entropy

The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function. Moreover, the probability distribution of the three-parameter entropy is derived which is expressed in terms of the translated logarithmic Lambert function.

math.CO↗
arXiv2021

Hankel Transform of the First Form (q,r)-Dowling Numbers

In this paper, the Hankel transform of the generalized q-exponential polynomial of the first form (q, r)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel transform of the first form (q, r)-Dowling numbers is obtained as special case.

math.CO↗
arXiv2020

Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers

In this paper, a q-analogue of r-Whitney-Lah numbers, also known as (q,r)-Whitney-Lah number, denoted by $L_{m,r}[n,k]_q$ is defined using the triangular recurrence relation. Several fundamental properties for the q-analogue are established such as vertical and horizontal recurrence relations, horizontal and exponential generating functions. Moreover, an explicit formula for (q,r)-Whitney-Lah number is derived using the concept of q-difference operator, particularly, the q-analogue of Newton's Interpolation Formula (the umbral version of Taylor series). Furthermore, an explicit formula for the first form (q,r)-Dowling numbers is obtained which is expressed in terms of (q,r)-Whitney-Lah numbers and (q,r)-Whitney numbers of the second kind.

math.CO↗
arXiv2020

Logarithmic Generalization of the Lambert W function and its Applications to Adiabatic Thermostatics of the Three-Parameter Entropy

A generalization of the Lambert W function called the logarithmic Lambert function is found to be a solution to the thermostatics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula and branches of the function are obtained. The thermostatics are computed and the heat functions are expressed in terms of the logarithmic Lambert function.

math.CO↗
arXiv2020

Higher Order Apostol-Type Poly-Genocchi Polynomials with Parameters a, b and c

In this paper, a new form of poly-Genocchi polynomials is defined by means of poly-logarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials is introduced that possesses a double generating function. Finally, the type 2 Apostol-poly-Genocchi polynomials with parameters a, b and c are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.

math.CO↗
arXiv2020

Three-Parameter Logarithm and Entropy

A three-parameter logarithmic function is derived using the notion of q-analogue and ansatz technique. The derived three-parameter logarithm is shown to be a generalization of the two-parameter logarithmic function of Schwammle and Tsallis as the latter is the limiting function of the former as the added parameter goes to 1. The inverse of the three-parameter logarithm and other important properties are also proved. A three-parameter entropic function is then defined and is shown to be analytic and hence Lesche-stable, concave and convex in some ranges of the parameters.

cond-mat.stat-mech↗
arXiv2019

A Combinatorial Analysis Of Higher Order Generalised Geometric Polynomials: A Generalisation Of Barred Preferential Arrangements

A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer a generalisation of barred preferential arrangements by making use of the generalised Stirling numbers proposed by Hsu and Shiue (1998). We discuss how these generalised barred preferential arrangements offer a unified combinatorial interpretation of geometric polynomials. We also discuss asymptotic properties of these numbers.

math.CO↗
arXiv2019

A $q$-Analogue of $r$-Whitney Numbers of the Second Kind and Its Hankel Transform

A $q$-analogue of $r$-Whitney numbers of the second kind, denoted by $W_{m,r}[n,k]_q$, is defined by means of a triangular recurrence relation. In this paper, several fundamental properties for the $q$-analogue are established including other forms of recurrence relations, explicit formulas and generating functions. Moreover, a kind of Hankel transform for $W_{m,r}[n,k]_q$ is obtained.

math.CO↗
arXiv2018

Analogies of the Qi formula for some Dowling type numbers

In the paper, the authors establish explicit formulas for the Dowling numbers and their generalizations in terms of generalizations of the Lah numbers and the Stirling numbers of the second kind. These results gen- eralize the Qi formula for the Bell numbers in terms of the Lah numbers and the Stirling numbers of the second kind.

math.CO↗
arXiv2016

On Multi Poly-Bernoulli Polynomials

In this paper, we define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi poly-Bernoulli polynomials is established using the $r$-Whitney numbers of the second kind.

math.CO↗
arXiv2016

Rook theoretic proofs of some identities related to Spivey's Bell number formula

We use rook placements to prove Spivey's Bell number formula and other identities related to it, in particular, some convolution identities involving Stirling numbers and relations involving Bell numbers. To cover as many special cases as possible, we work on the generalized Stirling numbers that arise from the rook model of Goldman and Haglund. An alternative combinatorial interpretation for the Type II generalized $q$-Stirling numbers of Remmel and Wachs is also introduced in which the method used to obtain the earlier identities can be adapted easily.

math.CO↗
arXiv2015

On Generalized Multi Poly-Euler and Multi Poly-Bernoulli Polynomials

In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are defined using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. These are generalized further using the concept of Hurwitz-Lerch multiple zeta values.

math.NT↗
arXiv2015

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.

math.NT↗
arXiv2014

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.

math.NT↗