Geodesic
Integral estimates for Laguerre polynomials with exponential weight function
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2020), pp. 16-25.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider the system of functions $\lambda_{1+n}(x)$ generated by the system of Laguerre function. For the functions $\lambda_{1+n}(x)$ different representations in terms of the Laguerre polynomials $L_n^\alpha(x)$ are obtained. Using these representations and asymptotic formulas for the $L_n^\alpha(x)$ polynomials, we investigated the behavior of the functions $\lambda_{1+n}(x)$ on $[0,\infty)$ as $n\rightarrow\infty$ and obtained estimates similar to those for the Laguerre functions
Mots-clés : Laguerre polynomials, Laguerre functions
Keywords: asymptotic properties. 
@article{IVM_2020_4_a1,
     author = {R. M. Gadzhimirzaev},
     title = {Integral estimates for {Laguerre} polynomials with exponential weight function},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--25},
     publisher = {mathdoc},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_4_a1/}
}
TY  - JOUR
AU  - R. M. Gadzhimirzaev
TI  - Integral estimates for Laguerre polynomials with exponential weight function
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 16
EP  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_4_a1/
LA  - ru
ID  - IVM_2020_4_a1
ER  - 
%0 Journal Article
%A R. M. Gadzhimirzaev
%T Integral estimates for Laguerre polynomials with exponential weight function
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 16-25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_4_a1/
%G ru
%F IVM_2020_4_a1
R. M. Gadzhimirzaev. Integral estimates for Laguerre polynomials with exponential weight function. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2020), pp. 16-25. http://geodesic.mathdoc.fr/item/IVM_2020_4_a1/

[1] Gadzhimirzaev R.M., “Sobolev-orthonormal system of functions generated by the system of Laguerre functions”, Probl. Anal. Issues Anal., 8(26):1 (2019), 32–46 | DOI | MR | Zbl

[2] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[3] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii., v. 2, Nauka, M., 1966

[4] Brychkov Yu.A., Spetsialnye funktsii. Proizvodnye, integraly, ryady i drugie formuly, Spravochnik, Fizmatlit, M., 2006

[5] Erdélyi A., “Asymptotic forms for Laguerre polynomials”, J. Indian Math. Soc., 24 (1960), 235–250 | MR

[6] Askey R., Wainger S., “Mean convergence of expansions in Laguerre and Hermite series”, Amer. J. Math., 87 (1965), 698–708 | DOI | MR

[7] Fikhtengolts G.M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Fizmatlit, M., 2001