Complementary Romanovski–Routh Polynomials, Orthogonal Polynomials on the Unit Circle, and Extended Coulomb Wave Functions

Martínez–Finkelshtein, Andrei; Ribeiro, Luana L. Silva; Ranga, A. Sri; Tyaglov, Mikhail

doi:10.1007/s00025-020-1167-8

Cited by 3 publications

(2 citation statements)

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“…Such polynomials are shown to be related to a special class of orthogonal polynomials on the unit circle. Also, these are useful in the study of Schrődinger equations, regular Coulomb wave functions and extended regular Coulomb wave functions [23,24]. Interested authors may look at [4,5,18] and references therein for some recent progress related to R II type recurrence relations and R II polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…. , x m )[24] is given byE = − 1≤j≤i≤m ln |x i − x j | + ζ m ln |x j − i| + ln |x i + i|] − θ m j=1 arctan(x j ).where the electrostatic field consists of i and −i two fixed negative charges of size ζ m , m movable positive unit charges and an external energy field of arctan type. In [23, Theorem 3.1], it was shown that the set {x m 1 (e), x m 2 (e) .…”

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confidence: 99%

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Chain sequences and Zeros of a perturbed $R_{II}$ type recurrence relation

Shukla¹,

Swaminathan²

2022

Preprint

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In this manuscript, new algebraic and analytic aspects of the orthogonal polynomials satisfying R II type recurrence relation given bywhere λ n is a positive chain sequence and a n , b n , c n are sequences of real or complex numbers with P −1 (x) = 0 and P 0 (x) = 1 are investigated when the recurrence coefficients are perturbed. Specifically, representation of new perturbed polynomials (co-polynomials of R II type) in terms of original ones with the interlacing and monotonicity properties of zeros are given. For finite perturbations, a transfer matrix approach is used to obtain new structural relations. Effect of co-dilation in the corresponding chain sequences and their consequences onto the unit circle are analysed. A particular perturbation in the corresponding chain sequence called complementary chain sequences and its effect on the corresponding Verblunsky coefficients is also studied.

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