A Note on the Trinomial Analogue of Bailey's Lemma

Recently, Andrews and Berkovich introduced a trinomial version of Bailey’s lemma. In this note we show that each ordinary Bailey pair gives rise to a trinomial Bailey pair. This largely widens the applicability of the trinomial Bailey lemma and proves some of the identities proposed by Andrews and Berkovich. The trinomial Bailey lemma In a recent paper, Andrews and Berkovich (AB) proposed a trinomial analogue of Bailey’s lemma [1]. As starting point AB take the following definitions of the q-trinomial coefficients ( L;B; q A )