Asymptotic behaviour of Ramanujan's tenth order mock theta functions
Following the method used earlier by \textit{G. E. Andrews} and \textit{D. Hickerson} [Adv. Math. 89, 60-105 (1991; Zbl 0739.11042)] for the sixth-order mock-theta functions and by \textit{G. N. Watson} [Proc. Lond. Math. Soc. (2) 42, 274-304 (1936; Zbl 0015.30402)] for the fifth-order mock-theta functions, the author shows that Ramanujan's four additional mock-theta functions are bounded near certain roots of unity. These four additional mock-theta functions of Ramanujan were called the tenth-order mock-theta functions by \textit{Y.-S. Choi} [Invent. Math. 136, 497-569 (1999; Zbl 0951.33013); Adv. Math. 156, 180-285 (2000; Zbl 0984.33007)]. Several other interesting results for these tenth-order mock-theta functions are also proven here.
scientific article; zbMATH DE number 1881042