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

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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/}
}
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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/