# Note on the problem of Ramanujan’s radial limits

@article{Chen2014NoteOT, title={Note on the problem of Ramanujan’s radial limits}, author={Bin Chen and Haigang Zhou}, journal={Advances in Difference Equations}, year={2014}, volume={2014}, pages={1-11} }

AbstractRamanujan in his deathbed letter to GH Hardy concerned the asymptotic properties of modular forms and mock theta functions. For the mock theta function f(q), he claimed that as q approaches an even order 2k root of unity ζ,
limq→ζ(f(q)−(−1)k(1−q)(1−q3)(1−q5)⋯(1−2q+2q4−⋯))=O(1),
where (1−q)(1−q3)(1−q5)⋯(1−2q+2q4−⋯)=∏n=1∞1−qn(1+qn)2. Recently, Folsom, Ono and Rhoades have proved two closed formulas for the implied constant and formulated an open problem which is related to their two…

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The number of strongly unimodal sequences of weight n is denoted by u∗(n)$u^{*}(n)$. The generating functions for {u∗(n)}n=1∞$\{u^{*}(n)\}_{n=1}^{\infty}$ are…

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Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q…

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Abstract Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$…

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Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right)$ , where $\left| q \right|<1$ . He called them mock theta functions, because as $q$ radially approaches any…