# About a partial theta function

Abstract : 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.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00866121
Submitted on : Thursday, September 26, 2013 - 9:12:27 AM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM

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• HAL Id : hal-00866121, version 1