Factors of some truncated basic hypergeometric series

Abstract

We prove that certain basic hypergeometric series truncated at $k=n-1$ have the factor ${\Phi }_n(q{)}^2$, where ${\Phi }_n(q)$ is the $n$-th cyclotomic polynomial. This confirms two recent conjectures of the author and Zudilin. We also put forward some conjectures on $q$-congruences modulo ${\Phi }_n(q{)}^2$.

9 pages

References in corpus (1)

• Some q-analogues of supercongruences of Rodriguez-Villegas