About a partial theta function
Résumé
Partial theta functions are of interest to statistical physics and combinatorics, to Ramanujan type $q$-series, to asymptotic analysis and to the theory of (mock) modular forms. One such function is de ned by the series $g_q(x) :=\sum _{k=0}^{\infty}q^{k^2}x^k$. We study the real analytic in $(-1, 1)$ function $-1+2g_q(-1)$ which appears in paper [4] when the relationship of partial theta functions and real rooted polynomials is considered. [4] Kostov V. P., B. Shapiro. Duke Math. J., 162, 2013, No 5, 825-861.