∞ n=0 pn(x)t n or, equivalently, p′n(x) = pn−1(x). If g(t) is an entire function, g(0) 6= 0, with at least one zero, the asymptotics of linearly scaled polynomials {pn(nx)} are described by means of finitely zeros of g, including those of minimal modulus. As a consequence, we determine the limiting behavior of their zeros as well as their density. The techniques and results extend our earlier w...

In this paper, we introduce a class of new classes degenerate unified polynomials and show some algebraic differential properties. This includes the Appell-type classical their most relevant generalizations. Most results are proved by using generating function methods illustrate our with examples.

In this paper, the class of (p,q)-Bessel-Appell polynomials is introduced. The generating function, series definition and determinant are established. Certain members considered some properties these also derived. Further, 2D introduced by means function definition. addition, graphical representations plotted with help Matlab.

Six approaches to the theory of Bernoulli polynomials are known; these are associated with the names of J. Bernoulli [2], L. Euler [4], E. Lucas [8], P. E. Appell [1], A. Hürwitz [6] and D. H. Lehmer [7]. In this note we deal with a new determinantal definition for Bernoulli polynomials recently proposed by F. Costabile [3]; in particular, we emphasize some consequent procedures for automatic c...