New contiguous relations for a balanced q-series and their applications
摘要
The present paper is mainly concerned with a balanced partial q-series. By the classical Abel lemma on summation by parts, we establish the q-contiguous relations for the partial sum whose iterating cases embrace many new summation and transformation formulae as well as some known results. Of particular interest are one identity of Rogers–Ramanujan type and two identities of partial theta functions.