Basic hypergeometric expressions for q-Tangent and q-Secant Numbers

When/Where:

February 27, 2018, 3:00 — 3:50 pm at LIT 368.

Abstract:

We derive new expressions for the generating functions of q-tangent and q-secant numbers from enumerating path diagrams given by Dyck paths together with partial fillings below the paths. In doing so, we provide expressions for path diagrams with restricted height involving basic hypergeometric functions, obtained by solving recurrences arising from the continued fraction representation of the generating functions.