DOI QR코드

DOI QR Code

A COMPREHENSIVE STUDY OF SECOND ORDER MOCK THETA FUNCTIONS

  • Published : 2005.11.01

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 $F_q$-functions.

Keywords

References

  1. G. E. Andrews, Hecke Modular forms and the Kac-Peterson identities, Trans Amer. Math. Soc. 283 (1984), 451-458 https://doi.org/10.2307/1999140
  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 https://doi.org/10.1016/0001-8708(91)90083-J
  4. Youn-Seo Choi, Tenth order mock theta functions in Ramanujan's 'Lost' Note- book, Invent. Math. 136 (1999), 497-569 https://doi.org/10.1007/s002220050318
  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 https://doi.org/10.1112/S0024610700008735
  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