53 citations · 108 across the 26 of their papers we have counts for
11 papers · 1 filter
Recent Advances in Asymptotic Analysis
R. Wong, Yu-Qiu Zhao
This is a survey article on an old topic in classical analysis. We present some new developments in asymptotics in the last fifty years. We start with the classical method of Darbo…
Isomonodromy sets of accessory parameters for Heun class equations
Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao
In this paper, we consider the monodromy and, in particularly, the isomonodromy sets of accessory parameters for the Heun class equations. We show that the Heun class equations can…
Asymptotics of the Charlier polynomials via difference equation methods
Xiao-Min Huang, Yu Lin, Yu-Qiu Zhao
We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit i…
Real solutions of the first Painlevé equation with large initial data
Wen-Gao Long, Yu-Tian Li, Sai-Yu Liu +1
We consider three special cases of the initial value problem of the first Painlevé equation (PI). Our approach is based on the method of uniform asymptotics introduced by Bassom, C…
Hankel determinants for a singular complex weight and the first and third Painlevé transcendents
Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao
In this paper, we consider polynomials orthogonal with respect to a varying perturbed Laguerre weight for and on certain contours in the complex pl…
Proof of a conjecture of Granath on optimal bounds of the Landau constants
Chun-Ru Zhao, Wen-Gao Long, Yu-Qiu Zhao
We study the asymptotic expansion for the Landau constants , \begin{equation*} πG_{n}\sim \ln(16N)+γ+\sum^{\infty}_{k=1}\frac{α_k}{N^k} ~~\mbox{as} ~ n\rightarrow\infty, \end{…
Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation
Zhao-Yun Zeng, Yu-Qiu Zhao
We apply the uniform asymptotics method proposed by Bassom, Clarkson, Law and McLeod to a special Painlevé V equation, and we provide a simpler and more rigorous proof of the conne…
Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point
Xiao-Bo Wu, Yu Lin, Shuai-Xia Xu +1
In this paper, we develop the Riemann-Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point. To illustrate our met…
Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao
In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight , , and . When the matr…
Asymptotics of Landau constants with optimal error bounds
Yutian Li, Saiyu Liu, Shuaixia Xu +1
We study the asymptotic expansion for the Landau constants where , $…
Uniform Treatment of Darboux's Method and the Heisenberg Polynomials
Sai-Yu Liu, R. Wong, Yu-Qiu Zhao
We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux's method.