Asymptotics for solutions of smooth recurrence equations

Mate, Attila; Nevai, Paul

doi:10.1090/s0002-9939-1985-0773995-6

Cited by 7 publications

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References 10 publications

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“…see Nevai and Máté,31 and relationship between orthogonal and orthonormal, See Chen and Ismail. 20 We find, if the integer n is sufficiently large, that n+1 n > 1, thus, n+1 > n if integer n is fully large.…”

Section: (53)mentioning

confidence: 68%

On semiclassical orthogonal polynomials associated with a Freud‐type weixght

Wang

Zhu

Chen

2020

Math Methods in App Sciences

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The recursion relationship: zP n (z) = P n+1 (z) + n P n−1 (z), n = 0, 1, 2 … is satisfied by all monic orthogonal polynomials in regard to an arbitrary Freud-type weight function. In current paper, one focuses on the weight functionto analyze its relative n and P n (z). Through above equation and orthogonality, we find that n (t) satisfy the first discrete Painlevé equation I Hierarchy and a high-order differential-difference equation, respectively. Then, we find that the asymptotic value of n is settled by Coulomb fluid. Additionally, we talk about P n (z) with = 0, including approximation for P n (0) and P ′ n (0), and bounds for P n (z) as n → ∞ are settled. KEYWORDS asymptotics, bounds, Freud-type weight, orthogonal polynomials, semiclassical MSC CLASSIFICATION 33C47; 34M55; 35C20; 65Q99 (z) = |z| e −z 6 +tz 2 ,where both z and t belonged to R, and > −1.Remark 1.1.(2) is a Freud-type weight, see Olver et al. 5Math Meth Appl Sci. 2020;43:5295-5313. wileyonlinelibrary.com/journal/mma

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Section: (53)mentioning

confidence: 68%