27 citations · 62 across the 20 of their papers we have counts for
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Error bounds for the asymptotic expansions of the Jacobi polynomials
Xiao-Min Huang, Yu Lin, Xiang-Sheng Wang +1
This paper aims to derive explicit and computable error bounds for the asymptotic expansion of the Jacobi polynomials as their degree approaches infinity, using an integral method.…
Orthogonal polynomials with periodic recurrence coefficients
Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang
In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating fun…
Asymptotics, orthogonality relations and duality for the and -symmetric polynomials in the -Askey scheme
Howard S. Cohl, Roberto S. Costas-Santos, Xiang-Sheng Wang
In this survey we summarize the current state of known orthogonality relations for the and -symmetric and dual subfamilies of the Askey--Wilson polynomials in the -A…
Error bounds for the asymptotic expansions of the Hermite polynomials
Wei Shi, Gergő Nemes, Xiang-Sheng Wang +1
In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel--Rotach scale. Three cases, depending on whe…
Supercritical Hopf Bifurcation of Cooperative Predation
Srijana Ghimire, Xiang-Sheng Wang
In this work, we conduct a rigorous analysis on the dynamics of a predator-prey model with cooperative predation. From the root classification of an algebraic equation, we derive e…
Bivariate Lagrange interpolation at the checkerboard nodes
Lihua Cao, Srijana Ghimire, Xiang-Sheng Wang
In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set of checkerboard nodes. This formula generalizes existing results of bivar…
Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
Dan Dai, Weiying Hu, Xiang-Sheng Wang
In this paper, we study a family of orthogonal polynomials arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only,…
Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients
Xiang-Sheng Wang
In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the…
Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems
Dan Dai, Mourad E. H. Ismail, Xiang-Sheng Wang
We study the Plancherel--Rotach asymptotics of four families of orthogonal polynomials, the Chen--Ismail polynomials, the Berg-Letessier-Valent polynomials, the Conrad--Flajolet po…
Global Asymptotics of the Meixner Polynomials
X. -S. Wang, R. Wong
Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. {\bf 137}(1993), 295-368], we derive asymptotic formulas for the…