Proofs of five conjectures on matching coefficients of Baruah, Das and Schlosser by an algorithmic approach (Q2100055)

Very recently, it was observed that the series expansions of certain infinite \(q\)-products have matching coefficients with their reciprocals. In this paper, the authors present an algorithm on vanishing coefficients with arithmetic progressions in the sum of two generalized eta-quotients by using the theory of modular forms. They utilize this algorithm to prove five conjectures on matching coefficients in series expansions of certain \(q\)-products and their reciprocals. One of these conjectures was provided by \textit{N. D. Baruah} and \textit{H. Das} [Ramanujan J. 59, No. 2, 511--548 (2022; Zbl 07589229)], and the others were found by Schlosser.