Note on power sums of the zeros of certain Laguerre and Bessel polynomials

Komarov, M. A.

doi:10.1080/10652469.2019.1709455

Integral Transforms and Special Functions

2020

DOI: 10.1080/10652469.2019.1709455

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Note on power sums of the zeros of certain Laguerre and Bessel polynomials

M. A. Komarov

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Cited by 2 publications

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Rate of approximation of zf′(z) by special sums associated with the zeros of the Bessel polynomials

Komarov

2020

Indagationes Mathematicae

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Let α n1 , . . . , α nn be the zeros of the nth Bessel polynomial y n (z) and let a nk = 1 − α nk /2, b nk = 1 + α nk /2 (k = 1, . . . , n). We propose the new formulaThis formula is exact for all polynomials of degree at most 2n. We find the sharp order of nonlocal estimate of the corresponding remainder for the case when all |f m | ≤ 1. The estimate shows a high rate of convergence of the differentiating sums to zf ′ (z) on compact subsets of the open unit disk, namely, O(0.85 n n 1−n ) as n → ∞.

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Rate of approximation of zf′(z) by special sums associated with the zeros of the Bessel polynomials

Komarov

2020

Indagationes Mathematicae

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An Introductory Overview of Bessel Polynomials, the Generalized Bessel Polynomials and the q-Bessel Polynomials

Srivástava

2023

Symmetry

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Named essentially after their close relationship with the modified Bessel function Kν(z) of the second kind, which is known also as the Macdonald function (or, with a slightly different definition, the Basset function), the so-called Bessel polynomials yn(x) and the generalized Bessel polynomials yn(x;α,β) stemmed naturally in some systematic investigations of the classical wave equation in spherical polar coordinates. Our main purpose in this invited survey-cum-expository review article is to present an introductory overview of the Bessel polynomials yn(x) and the generalized Bessel polynomials yn(x;α,β) involving the asymmetric parameters α and β. Each of these polynomial systems, as well as their reversed forms θn(x) and θn(x;α,β), has been widely and extensively investigated and applied in the existing literature on the subject. We also briefly consider some recent developments based upon the basic (or quantum or q-) extensions of the Bessel polynomials. Several general families of hypergeometric polynomials, which are actually the truncated or terminating forms of the series representing the generalized hypergeometric function rFs with r symmetric numerator parameters and s symmetric denominator parameters, are also investigated, together with the corresponding basic (or quantum or q-) hypergeometric functions and the basic (or quantum or q-) hypergeometric polynomials associated with rΦs which also involves r symmetric numerator parameters and s symmetric denominator parameters.

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Note on power sums of the zeros of certain Laguerre and Bessel polynomials

Cited by 2 publications

References 9 publications

Rate of approximation of zf′(z) by special sums associated with the zeros of the Bessel polynomials

Rate of approximation of zf′(z) by special sums associated with the zeros of the Bessel polynomials

An Introductory Overview of Bessel Polynomials, the Generalized Bessel Polynomials and the q-Bessel Polynomials

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