Beih S. El-Desouky

Generalized higher order Stirling numbers

In this paper new explicit expressions for both kinds of Comtet numbers and some interesting special cases are derived. Moreover, we define and study the generalized multiparameter non-central Stirling numbers and generalized Comtet numbers via differential operators. Furthermore, recurrence relations and new explicit formulas for those numbers are obtained. Finally some interesting special cases, new combinatorial identities and a connection between these numbers and some interesting polynomials are deduced.

A new unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials

In this paper, we introduce a new unified family of polynomials including unified Apostol-Bernoulli, Euler and Genocchi polynomials, see Luo and Srivastava (2006) and a unified family of polynomials defined by Ozden et al. (2010). Also, by applying the Mellin transformation for the generating function of the new unified family of polynomials, we deduced a unified class of zeta function. Finally, we derive some relationships between our new unified family of polynomials and some types of generalized polynomials.

q-Analogues of multiparameter non-central Stirling and generalized harmonic numbers

Abstract In this paper we derive q -analogues of the multiparameter non-central Stirling numbers of the first and second kind, introduced by El-Desouky. Moreover, recurrence relations, explicit formulas and a connection between these numbers and generalized q -harmonic numbers are obtained. Furthermore, some important special cases and new combinatorial identities are given. Finally, algorithms of these numbers and matrix representation using Maple are derived.

Odd Generalized Exponential Flexible Weibull Extension Distribution

In this article we introduce a new four parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and mode, the moment generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is given. Moreover, we give the advantage of the OGE-FWE distribution by an application using real data.