\(q\)-functional equations and some partition identities (Q1182306)

The author has used \(q\)-functional equations to prove some \((n+t)\) color partition identities. Generating functions for all odd-even partitions, odd-even partitions with \(\text{rank}\equiv 0\pmod 4\) and odd-even partitions with \(\text{rank}\equiv 2\pmod 4\) are also derived. These generating functions can be obtained by other methods, the methods used in this article indicate how nicely analysis and combinatorics interact in partition theory.