The study of polynomial sequences and their moment properties occupies a central role in contemporary mathematical research, bridging classical analysis with modern combinatorial theory. Polynomial ...

Abstract. We study the complex Hermite polynomials {Hm,n(z, z̄)} in some detail, establish operational formulas for them and prove a Kibble-Slepian type formula, which extends the Poisson kernel for ...

We discuss differential-difference properties of the extended Jacobi polynomials $$P_n(x) = _{p + 2}F_q(-n, n + \lambda, a_p; b_q; x)\quad (n = 0, 1,\ldots).$$ The ...

Roots can occur in a parabola in 3 different ways as shown in the diagram below: In diagram A, we can see that this parabola has 2 roots, diagram B has 1 root and diagram C has no roots. What type of ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...