97 citations · 499 across the 139 of their papers we have counts for
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New degenerated polynomials arising from non-classical Umbral Calculus
Orli Herscovici, Toufik Mansour
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbr…
Nonlinear differential equation for Korobov numbers
Dae San Kim, Taekyun Kim, Hyuck In Kwon +1
In this paper, we present nonlinear differential equations for the generating functions for the Korobov numbers and for the Frobenuius-Euler numbers. As an application, we find an…
A Digital Binomial Theorem for Sheffer Sequences
Toufik Mansour, Hieu D. Nguyen
We extend the digital binomial theorem to Sheffer polynomial sequences by demonstrating that their corresponding Sierpiński matrices satisfy a multiplication property that is equiv…
A -Digital Binomial Theorem
Toufik Mansour, Hieu D. Nguyen
We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.
Apostol-Euler polynomials arising from umbral calculus
Taekyun Kim, Toufik Mansour, Seog-Hoon Rim
In this paper, by using the orthogonality type as defined in the umbral calculus, we derive explicit formula for several well known polynomials as a linear combination of the Apost…
Average norms of polynomials
T. Mansour
In this paper we study the average $\NL_{2α}$-norm over -polynomials, where is a positive integer. More precisely, we present an explicit formula for the average $\NL_{2α}$-…