An asymptotic formula for the exponential polynomials and a central limit theorem for their coefficients (Q1059749)

In this paper an asymptotic formula for \(A_ n(x)\) defined as \[ \sum^{\infty}_{m=0}A_ m(x)(z^ m/m!)=\exp [x\{g(z)-g(0)\}], \] has been obtained and then the asymptotic normality of the combinatorial distribution \[ p(n;m,\lambda)=A(m,n)\lambda^ n/A_ m(\lambda),\quad n=0,1,...,m,\quad 0<a<\lambda <b \] has been established.