Asymptotic formulas for some retricted partition functions

We use Rademacher’s method to obtain asymptotic expressions for some restricted partition functions. For fixed positive integers m > 1 and l, we consider the number pm(n) of partitions of n into summands not divisible by m, and the number pml (n) of partitons of n with the further restriction that any integer occurs at most l times as a summand.