Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Complementary Romanovski-Routh polynomials and their zeros
View through CrossRef
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials. Following the renewed interest in quadrature formulas on the unit circle and RII type polynomials, in this work we present properties satisfied by the zeros of the complementary Romanovski-Routh polynomials. Our results include extreme bounds, convexity, density, and the connection of such zeros with the zeros of classical orthogonal polynomials via asymptotic formulas.
Brazilian Society for Computational and Applied Mathematics (SBMAC)
Title: Complementary Romanovski-Routh polynomials and their zeros
Description:
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials.
Following the renewed interest in quadrature formulas on the unit circle and RII type polynomials, in this work we present properties satisfied by the zeros of the complementary Romanovski-Routh polynomials.
Our results include extreme bounds, convexity, density, and the connection of such zeros with the zeros of classical orthogonal polynomials via asymptotic formulas.
Related Results
Long Journey from Stevenson’s Formally Complex Hypergeometric Polynomials to Real-by-Definition Romanovski-Routh Polynomials
Long Journey from Stevenson’s Formally Complex Hypergeometric Polynomials to Real-by-Definition Romanovski-Routh Polynomials
The paper reexamines Stevenson’s technique for solving Schrödinger’s “Kepler problem” in a spherical space in terms of formally complex hypergeometric polynomials. A certain advant...
Extending Romanovski polynomials in quantum mechanics
Extending Romanovski polynomials in quantum mechanics
Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Sca...
On the Elementary Symmetric Polynomials and the Zeros of Legendre Polynomials
On the Elementary Symmetric Polynomials and the Zeros of Legendre Polynomials
In this paper, we seek to present some new identities for the elementary symmetric polynomials and use these identities to construct new explicit formulas for the Legendre polynomi...
Solusi Persamaan Dirac Untuk Potensial Manning Rosen Hyperbolik Plus Potensial Tensor Tipe Coulomb Pada Pseudospin Simetri Menggunakan Polynomial Romanovski
Solusi Persamaan Dirac Untuk Potensial Manning Rosen Hyperbolik Plus Potensial Tensor Tipe Coulomb Pada Pseudospin Simetri Menggunakan Polynomial Romanovski
The relativistic energy and wave function for the hyperbolic Manning Rosen potential with Coulomb-type tensor potential in the case of pseudospin symmetry are obtained from solving...
On Convolved Fibonacci Polynomials
On Convolved Fibonacci Polynomials
This work delves deeply into convolved Fibonacci polynomials (CFPs) that are considered generalizations of the standard Fibonacci polynomials. We present new formulas for these pol...
Novel Formulas of Schröder Polynomials and Their Related Numbers
Novel Formulas of Schröder Polynomials and Their Related Numbers
This paper explores the Schröder polynomials, a class of polynomials that produce the famous Schröder numbers when x=1. The three-term recurrence relation and the inversion formula...
The generalized Routh array and a further simplification of the extended Routh array
The generalized Routh array and a further simplification of the extended Routh array
The well-known Routh Array settles the problem of stability of systems of differential equations with rral coefficients. The Extended Routh Array (ERA) is the complex counterpart o...
Zeros of modular forms and Faber polynomials
Zeros of modular forms and Faber polynomials
AbstractWe study the zeros of cusp forms of large weight for the modular group, which have a very large order of vanishing at infinity, so that they have a fixed number of finite ...