Uniform Asymptotic Formula for Orthogonal Polynomials with Exponential Weight
- 1 January 2000
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 31 (5) , 992-1029
- https://doi.org/10.1137/s0036141098344671
Abstract
Let {p(n) (x)}(n greater than or equal to 0) be the set of orthonormal polynomials with respect to the exponential weight w (x) = e(-v(x)), where v (x) = x(2m) + ... is a monic polynomial of degree 2 m with m greater than or equal to 2 and is even. An asymptotic approximation is obtained for p(n)(x), as n --> infinity, which holds uniformly for 0 less than or equal to x less than or equal to O(n(1/2m)). As a corollary, a three-term asymptotic expansion is also derived for the zeros of these polynomials.Keywords
This publication has 7 references indexed in Scilit:
- A Uniform Asymptotic Formula for Orthogonal Polynomials Associated with exp(−x4)Journal of Approximation Theory, 1999
- Fourier Series in Orthogonal PolynomialsPublished by World Scientific Pub Co Pte Ltd ,1999
- Asymptotics for solutions of systems of smooth recurrence equationsPacific Journal of Mathematics, 1988
- Plancherel-Rotach-type asymptotics for orthogonal polynomials associated with exp(−x66)Journal of Approximation Theory, 1987
- Asymptotics for the Greatest Zeros of Orthogonal PolynomialsSIAM Journal on Mathematical Analysis, 1986
- Asymptotic Expansions of Ratios of Coefficients of Orthogonal Polynomials with Exponential WeightsTransactions of the American Mathematical Society, 1985
- Asymptotics for Orthogonal Polynomials Associated with $\exp ( - x^4 )$SIAM Journal on Mathematical Analysis, 1984