Inequalities for orthonormal Laguerre polynomials

Ilia Krasikov

doi:10.1016/j.jat.2006.04.005

Inequalities for orthonormal Laguerre polynomials

Ilia Krasikov^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let M_k^α (x) = fenced(L_k^(α) (x))² e^{- x} x^{α + 1}, where L_k^(α) (x) is the orthonormal Laguerre polynomial of degree k. For α ≥ 24 we will establish the following inequality 10^{- 8} < k^{1 / 6} (k + α + 1)^{- 1 / 2} under(max, x ≥ 0) M_k^α (x) < 1444,where the upper bound holds for k ≥ 35, and the lower one for k ≥ 2 × 10¹⁰. Sharp pointwise estimates on M_k^α and related functions for x ≥ 0 are also given.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Journal of Approximation Theory
Volume	144
Issue number	1
DOIs	https://doi.org/10.1016/j.jat.2006.04.005
State	Published - Jan 2007
Externally published	Yes

Keywords

Laguerre polynomials
Orthogonal polynomials

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10.1016/j.jat.2006.04.005

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title = "Inequalities for orthonormal Laguerre polynomials",

abstract = "Let Mkα (x) = fenced(Lk(α) (x))2 e- x xα + 1, where Lk(α) (x) is the orthonormal Laguerre polynomial of degree k. For α ≥ 24 we will establish the following inequality 10- 8 < k1 / 6 (k + α + 1)- 1 / 2 under(max, x ≥ 0) Mkα (x) < 1444,where the upper bound holds for k ≥ 35, and the lower one for k ≥ 2 × 1010. Sharp pointwise estimates on Mkα and related functions for x ≥ 0 are also given.",

keywords = "Laguerre polynomials, Orthogonal polynomials",

author = "Ilia Krasikov",

year = "2007",

month = jan,

doi = "10.1016/j.jat.2006.04.005",

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AU - Krasikov, Ilia

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N2 - Let Mkα (x) = fenced(Lk(α) (x))2 e- x xα + 1, where Lk(α) (x) is the orthonormal Laguerre polynomial of degree k. For α ≥ 24 we will establish the following inequality 10- 8 < k1 / 6 (k + α + 1)- 1 / 2 under(max, x ≥ 0) Mkα (x) < 1444,where the upper bound holds for k ≥ 35, and the lower one for k ≥ 2 × 1010. Sharp pointwise estimates on Mkα and related functions for x ≥ 0 are also given.

AB - Let Mkα (x) = fenced(Lk(α) (x))2 e- x xα + 1, where Lk(α) (x) is the orthonormal Laguerre polynomial of degree k. For α ≥ 24 we will establish the following inequality 10- 8 < k1 / 6 (k + α + 1)- 1 / 2 under(max, x ≥ 0) Mkα (x) < 1444,where the upper bound holds for k ≥ 35, and the lower one for k ≥ 2 × 1010. Sharp pointwise estimates on Mkα and related functions for x ≥ 0 are also given.

KW - Laguerre polynomials

KW - Orthogonal polynomials

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VL - 144

SP - 1

EP - 26

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 1

ER -

Inequalities for orthonormal Laguerre polynomials

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Keywords

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