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Keldysh Institute preprints, 2018, 159, 24 pp. (Mi ipmp2518)  

Asymptotical basis of solutions of $q$-recurrence relations outside of the zone of clustering eigenvalues

A. I. Aptekarev, D. N. Tulyakov

Keldysh Institute of Applied Mathematics, Russian Academy of Science, Miusskaya Pl.4, Moscow 125047, Russian Federation

Abstract: A procedure for constructing expansions of the basis of solutions of a four-term recurrence relations with coefficitnts from the ring $\mathbb{Z}[q,1/q]$ is described. The fact that outside of the zone of the clustering eigenvalues these expansions are the asymptotical expansions is proven.

Keywords: $q$-polynomials; asymptotics of the polynomial sequences; requrrence relations; difference equations.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025


DOI: https://doi.org/10.20948/prepr-2018-159

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Full text: http:/.../preprint.asp?id=2018-159&lg=r
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UDC: 517.53+517.9

Citation: A. I. Aptekarev, D. N. Tulyakov, “Asymptotical basis of solutions of $q$-recurrence relations outside of the zone of clustering eigenvalues”, Keldysh Institute preprints, 2018, 159, 24 pp.

Citation in format AMSBIB
\Bibitem{AptTul18}
\by A.~I.~Aptekarev, D.~N.~Tulyakov
\paper Asymptotical basis of solutions of $q$-recurrence relations outside of the zone of clustering eigenvalues
\jour Keldysh Institute preprints
\yr 2018
\papernumber 159
\totalpages 24
\mathnet{http://mi.mathnet.ru/ipmp2518}
\crossref{https://doi.org/10.20948/prepr-2018-159}
\elib{https://elibrary.ru/item.asp?id=35385340}


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