Source: wikibot/hardy-littlewood-tauberian-theorem
= Hardy–Littlewood Tauberian theorem
{wiki=Hardy–Littlewood_Tauberian_theorem}
The Hardy–Littlewood Tauberian theorem is an important result in analytic number theory and summability theory. It provides a bridge between the growth conditions of a generating function and the convergence behavior of its associated series. In particular, it establishes conditions under which the summation of a series can be related to the growth of its generating function.