We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if (q r−tk, qmk−(r−tk) ; q mk)∞ (q r, qmk−r; qmk)∞ =: X∞ n=0 cnq n , for certain integers k, m s and t, where r = sm+t, then ckn−rs is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also give results for cases not covered by the theorems of Alladi and Gordon. We also give some interpretations of the analytic results in terms of integer partitions.
Journal of the Australian Mathematical Society
Australian Mathematical Society
McLaughlin, J. (2015). Further results on vanishing coefficients in infinite product expansions. Journal of the Australian Mathematical Society, 98(1) Retrieved from https://digitalcommons.wcupa.edu/math_facpub/72
Preprint version is available here.