VANISHING COEFFICIENTS IN FOUR QUOTIENTS OF INFINITE PRODUCT EXPANSIONS

Motivated by Ramanujan's continued fraction and the work of Richmond and Szekeres ['The Taylor coefficients of certain infinite products', Acta Sci. Math. (Szeged) 40(3-4) (1978), 347-369], we investigate vanishing coefficients along arithmetic progressions in four quotients of infinite product expansions and obtain similar results. For example, a(1)(5n + 4) = 0, where a(1)(n) is defined by (q, q(4):q(5))(infinity)(3)/(q(2),q(3):q(5))(infinity)(2) = Sigma(infinity)(n=0) a(1)(n)q(n).