scholarly journals A Uniform Asymptotic Formula for Orthogonal Polynomials Associated with exp(−x4)

1999 ◽  
Vol 98 (1) ◽  
pp. 146-166 ◽  
Author(s):  
Bo Rui ◽  
R. Wong
Keyword(s):  
Asymptotic Formula ◽  
Orthogonal Polynomials

An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials

1992 ◽  
Vol 35 (3) ◽  
pp. 381-389
Author(s):  
William B. Jones ◽  
W. J. Thron ◽  
Nancy J. Wyshinski
Keyword(s):  
Distribution Function ◽  
Asymptotic Formula ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Continued Fractions ◽  
Polynomial Sequence ◽  
Convergence Results ◽  
Compact Subsets

AbstractIt is known that the n-th denominators Qn (α, β, z) of a real J-fractionwhereform an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formulathe convergence being uniform on compact subsets of

scholarly journals On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1161
Author(s):  
Jorge A. Borrego-Morell ◽  
Cleonice F. Bracciali ◽  
Alagacone Sri Ranga
Keyword(s):  
Hilbert Space ◽  
Asymptotic Formula ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Morse Potential ◽  
Bound State ◽  
Orthogonal Basis ◽  
Dependent Potential ◽  
Energy Dependent ◽  
Class Of Functions

We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen–Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen–Morse potential, an identity involving Gegenbauer polynomials is obtained.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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