Hankel Determinant and Orthogonal Polynomials for a Perturbed Gaussian Weight: from Finite $n$ to Large $n$ Asymptotics

Chao Min, Yang Chen

We study the monic polynomials orthogonal with respect to a symmetric perturbed Gaussian weight $$w(x;t):={\mathrm{e}}^{-x^2}{\left(1+t{x}^2\right)}^{\lambda },x\in \mathbb{R},$$ wher…