4 papers
Stirling numbers with higher level and records
F. A. Shiha
In this present paper, we show that the Stirling numbers of the first kind with higher level connected with the probability distribution of the number of records and record times i…
The r-central factorial numbers with even indices
F. A. Shiha
In this paper, we introduce the -central factorial numbers with even indices of the first and second kind, as extended versions of the central factorial numbers with even indice…
An explicit Formula for Bernoulli Polynomials with a Parameter in Terms of -Whitney Numbers
F. A. Shiha
We define the Bernoulli polynomials with a parameter in terms of -Whitney numbers of the second kind. Some algebraic properties and combinatorial identities of these polynom…
Explicit Formulae of Cauchy Polynomials with a Parameter in Terms of -Whitney Numbers
F. A. Shiha
The Cauchy polynomials with a parameter were recently defined, and several arithmetical properties were studied. In this paper, we establish explicit formulae for computing the…