Partition Theorems Related to Some Identities of Rogers and Watson

This paper proves two general partition theorems and several special cases of each with both of the general theorems based on four q-series identities originally due to L. J. Rogers and G. N. Watson. One of the most interesting special cases proves that the number of partitions of an integer n into parts where even parts may not be repeated, and where odd parts occur only if an adjacent even part occurs is equal to the number of partitions of n into parts <!-- MATH $\equiv \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 7 \pmod 20$ --> . The companion theorem proves that the number of partitions of an integer n into parts where even parts may not be repeated, where odd parts 1$"> occur only if an adjacent even part occurs, and where 1's occur arbitrarily is equal to the number of partitions of n into parts <!-- MATH $\equiv \pm 1, \pm 2, \pm 5, \pm 6, \pm 8, \pm 9 \pmod 20$ --> .