Ramanujan’s fifth order and tenth order mock theta functions - a generalization


  • Bhaskar Srivastava University of Lucknow.




Mock theta function, q-Multibasic expansion, q-Integral.


A generalization of Ramanujan’s fifth order and tenth order mock theta functions is given. It is shown that these belong to the family of Fq-functions. Using the properties of Fq-functions, relationship is given between these generalized fifth order mock theta functions of the first group with the generalized functions of the second group. The same is done for the generalized functions of the tenth order. q-Integral representation and multibasic expansions are also given.

Author Biography

Bhaskar Srivastava, University of Lucknow.

Department of Mathematics and Astronomy.


[1] G. E. Andrews, The fifth and seventh order mock theta, Trans. Amer. Math. Soc. 293, pp. 113-134, (1986).

[2] G. E. Andrews, Mock Theta Functions, Proc. Sympos. Pure Math., 49, Part 2, pp. 283-298, (1989).

[3] Youn-Seo Choi, Tenth order mock theta functions in Ramanujan’s ‘Lost’ Notebook, Invent. Math. 136, pp. 497-569, (1999).

[4] Youn-Seo Choi, The basic bilateral hypergeometric series and the mock theta functions, Ramanujan J. 24, pp. 345-386, (2011).

[5] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, (1990).

[6] E. D. Rainville, Special Function, Chelsea Publishing Company, Bronx, New York, (1960).

[7] S. Ramanujan, Collected Paper, Cambridge University Press 1927, reprinted by Chelsea New York, (1962).

[8] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25, pp. 318-343, (1984).

[9] G. N. Watson, The final problem: An account of the mock theta functions, J. London Math. Soc. 11, pp. 55-80, (1936).

[10] G. N. Watson, The mock theta functions (2), Proc. London Math. Soc. (2) 42, pp. 274-304, (1937).

How to Cite

B. Srivastava, “Ramanujan’s fifth order and tenth order mock theta functions - a generalization”, Proyecciones (Antofagasta, On line), vol. 34, no. 3, pp. 277-296, 1.