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In 2010 Zagier introduced the notion of a quantum modular form. One of hisfirst examples was the "strange" function $F(q)$ of Kontsevich. Here we producea new example of a quantum modular form by making use of some of Ramanujan'smock theta functions. Using these functions and their transformation behaviour,we also compute asymptotic expansions similar to expansions of $F(q)$.

Asymptotic expansions, $L$-values and a new Quantum Modular Form