Refined $q$-Trinomial Coefficients and Two Infinite Hierarchies of $q$-Series Identities

27 Mar 2019  ·  Berkovich Alexander, Uncu Ali K. ·

We will prove an identity involving refined $q$-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined $q$-trinomials in an iterative fashion in the spirit of Bailey chains... One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem. read more

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Number Theory Combinatorics