Treffer: The 7-dissections of some infinite q-series expansions.

Recently, Kaur and Vandna verified several findings on the coefficients which vanish in certain infinite 푞-products for arithmetic progressions modulo 7. In this paper, we further produce the 7-dissections of three infinite 푞-products (− q , − q 6 ; q 7) ∞ (q 5 , q 9 ; q 14) ∞ 3 , (− q 2 , − q 5 ; q 7) ∞ (q 3 , q 11 ; q 14) ∞ 3 and, (− q 3 , − q 4 ; q 7) ∞ (q , q 13 ; q 14) ∞ 3 in the form of triple products. We have produced these results by generalising the method used to establish the results on the coefficients, which vanish in arithmetic progressions modulo 7. Moreover, from these 7-dissections, the coefficients which vanish in infinite 푞-products can identify readily. [ABSTRACT FROM AUTHOR]