 In particular, like modular forms, mock theta functions all lie in certain explicit finite-dimensional spaces, which reduces the long and hard proofs of many identities between them to routine linear algebra.For the first time it became possible to produce infinite number of examples of mock theta functions; before this work there were only about 50 examples known (most of which were first found by Ramanujan).As further applications of Zwegers's ideas, Kathrin Bringmann and Ken Ono showed that certain q-series arising from the Rogers–Fine basic hypergeometric series are related to holomorphic parts of weight 3/2 harmonic weak Maass forms and showed that the asymptotic series for coefficients of the order 3 mock theta function "f"("q") studied by and converges to the coefficients .