C. Adiga, T. Kim, D.-W. Park, Y. S. Ro and L.-C. Jang
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 9, 2003, Number 1, Pages 7—12
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Authors and affiliations
C. Adiga
Department of Studies in Mathematics University of Mysore
Mysore-570006, India
T. Kim
Institute of Science Education Kongju National University
Kongju-314-701, South Korea
D.-W. Park
Department of Mathematics Education Kongju National University
Kongju-314-701, South Korea
Y.S. Ro
Department of Mathematics Education Kongju National University
Kongju-314-701, South Korea
L-C.Jang
Department of Mathematics and Computer Science KonKuk University
Chungju 314-701, South Korea
Abstract
In this paper we establish continued fraction representations for theta functions, which are similar to q-continued fractions for certain q-products recorded by Ramanujan in the unorganized portions of his notebooks
Keywords
- q-continued fractions
- Theta-functions
AMS Classification
- 11A55
- 30B70
References
- C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Chapter 16 of Ramanujan’s second notebook: Theta-functions and q-series, Memoir No. 315, American Mathematical Society, Providence, 1985.
- C. Adiga, K. R. Vasuki and M. S. Mahadeva Naika, On some new identities involving integrals of theta-functions, Advan. Stud. Contemp. Math. 3 no. 2 (2001), 1-11.
- G. E. Andrews, B. C. Berndt, L. Jacobsen and R.L. Lamphere, The continued fractions found in the unorganized portions of Ramanujan’s notebooks, Memoir No. 477, American Mathematical Society, Providence, 1992.
- S. Bhargava and C. Adiga, On some continued fraction identities of Srinivasa Ramanujan, Proc. Amer. Math. Soc. 92 (1984), 13-18.
- W. B. Jones and W. J. Thron, Continued fractions: Analytic theory and applications, Addison- Wesley, Reading, 1980.
- 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- S. Ramanujan, The lost notebook and other unpublished papers, Narosa, New Delhi, 1988.
- H. S. Wall, Analytic Theory of continued fractions, D. Van Nostrand, Toronto, 1948.
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Cite this paper
Adiga, C., Kim, T., Park, D.-W., Ro, Y. S. & Jang, L.-C.. (2003). Continued fraction representations for theta functions. Notes on Number Theory and Discrete Mathematics, 9(1), 7-12.