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On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation

Kumar Devendra, Alghamdi Azza M.

Demonstratio Mathematica

2022

Vol. 55, nr 1

429--436

For an entire function solution of generalized bi-axisymmetric potential equation, we obtain a relationship between the generalized growth characteristics and polynomial approximation errors in sup norm by using the general functions introduced by Seremeta [On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. 88 (1970), no. 2, 291–301].

Analytical properties of the two-variables Jacobi matrix polynomials with applications

Abdalla Mohamed, Hidan Muajebah

Demonstratio Mathematica

2021

Vol. 54, nr 1

178--188

In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived. Furthermore, some relationships and applications are reported.

Integrals of legendre polynomials and solution of some partial differential equations

Belinsky R.

Journal of Applied Analysis

2000

Vol. 6, nr 2

259-282

We show a connection between the polynomials whose inflection points coincide with their interior roots (let us write shorter PIPCIR), Legendre polynomials, and Jacobi polynomials, and study some properties of PIPCIRs (Part I). In addition, we give new formulas for some classical orthogonal polynomials. Then we use PIPCIRs to solve some partial differential equations (Part II).