A COMPREHENSIVE STUDY OF SECOND ORDER MOCK THETA FUNCTIONS

Title & Authors
A COMPREHENSIVE STUDY OF SECOND ORDER MOCK THETA FUNCTIONS

Abstract
We consider the second order mock theta functions defined by McIntosh and define generalized functions. We give integral representation and multibasic expansion of these functions. We also show that they are $\small{F_q}$-functions.
Keywords
Mock theta functions;q-multibasic series;
Language
English
Cited by
1.
A Note on Continued Fractions and Mock Theta Functions,;;

Kyungpook mathematical journal, 2016. vol.56. 1, pp.173-184
References
1.
G. E. Andrews, Hecke Modular forms and the Kac-Peterson identities, Trans Amer. Math. Soc. 283 (1984), 451-458

2.
G. E. Andrews, B. C. Berndt, L. Jacobsen, and R. L. Lamphere, The continued fractions found in the Unorganised portions of Ramanujan's notebooks, Memoir no. 477, American Mathematical Society, Providence, 1992

3.
G. E. Andrews and D. Hickerson, Ramanujan's 'Lost' Notebook VII: The sixth order mock theta functions, Adv. Math. 89 (1991), 60-105

4.
Youn-Seo Choi, Tenth order mock theta functions in Ramanujan's 'Lost' Note- book, Invent. Math. 136 (1999), 497-569

5.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990

6.
B. Gordon and R. J. McIntosh, Some eight order mock theta functions, J. London Math. Soc. 62 (2000), no. 2, 321-335

7.
R. J. McIntosh, Second order mock theta function, submitted to Canad. J. Math. 2004

8.
E. D. Rainville, Special Function, Chelsea Publishing Company, Bronx, New York, 1960

9.
S. Ramanujan, Collected Paper, Cambridge University Press, London/New York 1927 (reprinted Chelsea New York, 1962)

10.
Bhaskar Srivastava, An application of the constant term method to Ramanujan's mock theta functions, accepted for publication

11.
C. Truesdell, An essay toward a unified theory of special functions, Princeton University Press, Princenton, 1948