ON ASYMPTOTIC FORMULAS FOR CERTAIN q-SERIES INVOLVING PARTIAL THETA FUNCTIONS.

In this article, we investigate the integer sequence ad(n), where for a positive integer d, ad(n) is defined by...In particular, we will present a combinatorial model for ad(n) via integer partitions and this will play a crucial role in obtaining an asymptotic formula for ad(n). Moreover, we will show that p(n) - 2ad(n) has an unexpected sign pattern via combinatorial arguments and asymptotic formulas. [ABSTRACT FROM AUTHOR]