The combinatorics of the leading root of the partial theta function

Thomas Prellberg

Recently Alan Sokal studied the leading root $x_0(q)$ of the partial theta function ${\Theta }_0(x,q)=\sum _{n=0}^{\infty }{x}^n{q}^{\left(\genfrac{}{}{0ex}{}{n}{2}\right)}$, considered as a formal power series. He pr…