Abstract
On page 9 in his Lost Notebook [232], Ramanujan offers eight identities for tenth order mock theta functions.
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G.E. Andrews and D. Hickerson, Ramanujan’s “Lost Notebook” VII: The sixth order mock theta functions, Adv. Math. 89 (1991), 60–105.
B.C. Berndt, Ramanujan’s Notebooks, Part I, Springer-Verlag, New York, 1985.
B.C. Berndt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991.
B.C. Berndt, Ramanujan’s Notebooks, Part IV, Springer-Verlag, New York, 1994.
B.C. Berndt and R.A. Rankin, Ramanujan: Letters and Commentary, American Mathematical Society, Providence, RI, 1995; London Mathematical Society, London, 1995.
Y.-S. Choi, Tenth order mock theta functions in Ramanujan’s lost notebook, Invent. Math. 136 (1999), 497–569.
Y.-S. Choi, Tenth order mock theta functions in Ramanujan’s lost notebook. II, Adv. Math. 156 (2000), 180–285.
Y.-S. Choi, Tenth order mock theta functions in Ramanujan’s lost notebook. IV, Trans. Amer. Math. Soc. 354 (2002), 705–733.
Y.-S. Choi, The basic bilateral hypergeometric series and the mock theta functions, Ramanujan J. 24 (2011), 345–386.
G. Gasper and M. Rahman, Basic Hypergeometric Series, 2nd. ed., Cambridge University Press, Cambridge, 2004.
B. Gordon and R.J. McIntosh, Some eighth order mock theta functions, J. London Math. Soc. (2) 62 (2000), 321–335.
B. Gordon and R.J. McIntosh, Modular transformations of Ramanujan’s fifth and seventh order mock theta functions, Ramanujan J. 7 (2003), 193–222.
B. Gordon and R.J. McIntosh, A survey of classical mock theta functions, in Partitions, q-Series and Modular Forms, K. Alladi and F. Garvan, eds., Develop. in Math. 23, 2011, Springer, New York, pp. 95–144.
D. Hickerson, A proof of the mock theta conjectures, Invent. Math. 94 (1988), 639–660.
D. Hickerson, On the seventh order mock theta functions, Invent. Math. 94 (1988), 661–677.
M.I. Knopp, Modular Functions in Analytic Number Theory, Markham, Chicago, 1970; reprinted by Chelsea, New York, 1993; reprinted by the American Mathematical Society, Providence, RI.
T.H. Koornwinder, On the equivalence of two fundamental theta identities, Anal. Applics. 12 (2014), 711–725.
R.J. McIntosh, Second order mock theta functions, Canad. Math. Bull. 50 (2) (2007), 284–290.
R.J. McIntosh, New mock theta conjectures, Part I, Ramanujan J. 46 (2018), 593–604.
L.J. Mordell, The value of the definite integral \(\int _{-\infty }^{\infty }{e^{at^{2}+bt } \over e^{ct} + d}dt\), Quart. J. Math. 48 (1920), 329–342.
S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
R.A. Rankin, Modular Forms and Functions, Cambridge University Press, Cambridge, 1977.
S. Robins, Generalized Dedekind η-products, Contemp. Math. 166 (1994), 119–128.
G.N. Watson, The final problem: An account of the mock theta functions, J. London Math. Soc. 11 (1936), 55–80; reprinted in [68], pp. 325–347.
E.T. Whittaker and G.N. Watson, A Course of Modern Analysis, 4th ed., Cambridge University Press, Cambridge, 1966.
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Andrews, G.E., Berndt, B.C. (2018). Transformation Formulas: 10th Order Mock Theta Functions. In: Ramanujan's Lost Notebook. Springer, Cham. https://doi.org/10.1007/978-3-319-77834-1_12
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