Probabilistic proofs of asymptotic formulas for some classical polynomials

Abstract

Recently Stadje [9] gave asymptotic formulas for some Bessel functions by using a probabilistic argument: some Bessel functions can be represented by the probability distribution of partial sums of symmetrized independent and identically distributed random variables (Feller [4], p. 149). Stadje used this idea and the local limit theorem, which is well known in probability theory.