3 problems

Let $q\to1$ in a basic hypergeometric integral, and let $c\geq0$ parameterize the scaling regime through factors of the form $\log (e^{-x\beta^c};e^{-\beta})_\infty$, where…

Let $r_n^{(\nu)}(x)$ be the polynomials introduced by the preceding recurrence, and let $s_n^{(\nu)}(x)$, $n\geqslant 0$, be the sequence uniquely defined by … with initial values…

Let $q=e^{-i\gamma}$ with $\gamma>0$, and let $\lambda$, $\mu$, $\nu$, and $z$ be parameters. Write…