Solutions of infinite order differential equations without the grouping phenomenon and a generalization of the Fabry-Polya theorem

摘要

Let {lambda n}(n=1)(similar to) be a sequence of distinct complex numbers diverging to infinity so that vertical bar lambda(n)vertical bar <= vertical bar lambda(n+1)vertical bar for all n is an element of N, and let {mu(n)}(n=1)(similar to) be a sequence of positive integers. Consider the set