CERTAIN ASYMPTOTIC EXPANSIONS FOR LAGUERRE POLYNOMIALS AND CHARLIER POLYNOMIALS

摘要

Here proposed are certain asymptotic expansion formulas for Ln(w-1)(λz) and Cn(ω)(λz) in whichO(λ) and n = 0(λ1/2 )(λ→∞) , z being x complex number. Also presented are certain estimates for the remainders(error bounds) of the asymptotic expansions within the regions D1( - ∞Rez≤1/2 (ω/λ) and D2(1/2 (ω/λ)≤Re.’C00)? respectively.