We briefly review the five possible real polynomial solutions of hypergeometric differential
equations. Three of them are the well known classical orthogonal polynomials, but the other …

In this paper, we consider spectral approximation of fractional differential equations (FDEs).
A main ingredient of our approach is to define a new class of generalized Jacobi functions …

The analytic solutions of the one-dimensional Schrödinger equation for the trigonometric
Rosen–Morse potential reported in the literature rely upon the Jacobi polynomials with …

The Schrödinger equation with the hyperbolic Scarf potential reported so far in the literature
is somewhat artificially manipulated into the form of the Jacobi equation with an imaginary …

In this paper we present a systematic way to describe exceptional Jacobi polynomials via
two partitions. We give the construction of these polynomials and restate the known aspects …

Abstract Using Casorati determinants of Hahn polynomials (hn α, β, N) n, we construct for
each pair F=(F 1, F 2) of finite sets of positive integers polynomials hn α, β, N; F, n∈ σ F …

The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for
computing both Caputo and (modified) Riemann–Liouville (RL) fractional pseudospectral …

We examine two binary operations on the set of algebraic polynomials, known as
multiplicative and additive finite free convolutions, specifically in the context of …

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials
P n α n β n are studied, assuming that 1\lim n → ∞ α _n n= A,\lim n → ∞ β _n n= B, with A …

We give a survey concerning both very classical and recent results on the electrostatic
interpretation of the zeros of some well-known families of polynomials, and the interplay …