Note on the problem of Ramanujan’s radial limits

Chen, Bin; Zhou, Haigang

doi:10.1186/1687-1847-2014-191

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2018

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“…As a result, they pointed out that Ramanujan’s claim is the special case of their theorem. The author and Zhou [ 18 ] established an inner relationship of the two theorems of Folsom–Ono–Rhoades.…”

Section: Introductionmentioning

confidence: 99%

Mock theta functions and Appell–Lerch sums

Chen

2018

J Inequal Appl

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Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function . The purpose of this paper is to consider the bilateral series for the universal mock theta function . As a result, we present the bilateral series associated with the odd order mock theta functions in terms of Appell–Lerch sums. A very interesting congruence relationship of the bilateral series for the third order mock theta function is established. The inner relationships between the two-group bilateral series of the fifth order mock theta functions are obtained as applications.

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Section: Introductionmentioning

confidence: 99%