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Integral Estimates for Laguerre Polynomials with Exponential Weight Function

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Abstract

We study the system of functions λ1+n(x) generated by the system of Laguerre functions. We express functions λ1+n(x) in terms of Laguerre polynomials \(L_n^\alpha (x)\). Using the obtained representations and asymptotic formulas for polynomials \(L_n^\alpha (x)\), we study the behavior of functions λ1+n(x) on [0,∞) with n →∞ and deduce estimates analogous to those for Laguerre functions.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-31-00477 mol_a.

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Authors and Affiliations

  1. Dagestan Federal Research Center of the Russian Academy of Sciences, 45 M. Gadjieva str., Makhachkala, 367000, Russia

    R. M. Gadzhimirzaev

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  1. R. M. Gadzhimirzaev
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Correspondence to R. M. Gadzhimirzaev.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 4, pp. 16–25.

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Gadzhimirzaev, R.M. Integral Estimates for Laguerre Polynomials with Exponential Weight Function. Russ Math. 64, 12–20 (2020). https://doi.org/10.3103/S1066369X20040027

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  • DOI: https://doi.org/10.3103/S1066369X20040027

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