Continued fraction representations for theta functions

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
Full paper (PDF, 177 Kb)

Details

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

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3. 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.
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8. H. S. Wall, Analytic Theory of continued fractions, D. Van Nostrand, Toronto, 1948.