Summation Formulae for Quintic <i>q</i>-Series

Abstract

By utilizing the modified Abel lemma on summation by parts, we examine a class of quintic q-series, that have close connections to the “twisted cubic q-series”. Several remarkable summation and transformation formulae are established. The related reversal series are also reviewed briefly.

Keywords

• basic hypergeometric series
• twisted cubic <i>q</i>-series
• quintic <i>q</i>-series
• reversal series
• Abel’s lemma on summation by parts