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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.34 no.3 Antofagasta set. 2015

http://dx.doi.org/10.4067/S0716-09172015000300006 

 

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

Bhaskar Srivastava

University of Lucknow, India.


ABSTRACT

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.

Subjclass : [2000]33D15.

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


REFERENCES

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

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

[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).         [ Links ]

[5]    G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, (1990). 2        [ Links ]

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

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

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

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

Bhaskar Srivastava

Department of Mathematics and Astronomy

University of Lucknow

Lucknow,

India

e-mail : bhaskarsrivastav@yahoo.com

Received : January 2015. Accepted : July 2015

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