Global asymptotic expansions of the Laguerre polynomials -- a Riemann-Hilbert approach
The authors derive two asymptotic expansions of the Laguerre polynomials, one holds uniformly in the right half plane while the other is true in the left half plane such that the two taken together cover the entire complex \(z\)-plane. The steepest descent method for Riemann-Hilbert problems has been used to establish the main results. The domains of validity of the results of the paper are considerably larger than those of the existing expansions.
scientific article; zbMATH DE number 5549474
scientific article