On the equivalence of Ramanujan's partition identities and a connection with the Rogers-Ramanujan continued fraction

Journal of Mathematical Analysis and Applications

Volumn 198, Issue 1, 1996, Pages 111-120

  Chan, Heng Huat ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030584352     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0071     Document Type: Article

References (13)

1. 1. T. M. Apostol, "Introduction to Analytic Number Theory," Springer-Verlag, New York, 1986.
2. 2. H. H. Chan, New proofs of Ramanujan's partition identities for moduli 5 and 7, J. Number Theory, to appear.
3. 3. K. Chandrasekharan, "Elliptic Functions," Springer-Verlag, New York, 1985.
4. 4. E. T. Copson, "Theory of Functions of a Complex Variable," Oxford Univ. Press, London, 1935.
5. 5. G. H. Hardy and E. M. Wright, "An Introduction to the Theory of Numbers," Oxford Univ. Press, New York, 1988.
6. 6. E. Landau, "Elementary Number Theory," Chelsea, New York, 1958.
7. 7. A. Ogg, "Modular Forms and Dirichlet Series," Benjamin, New York, 1969.
8. 8. S. Raghavan, On certain identities due to Ramanujan, Quart. J. Math. Oxford (2) 37 (1986), 221-229.
9. 9. S. Ramanujan, "The Lost Notebook of Other Unpublished Papers," Narosa, New Delhi, 1988.
10. 10. S. Ramanujan, Some properties of p(n), the number of partitions of n, Proc. Cambridge Philos. Soc. 19 (1918), 207-210.
11. 11. C. L. Siegel, A simple proof of η(-1/τ) = η(τ)√τ/i, Mathematika 1 (1954).
12. 12. L. C. Washington, "Introduction to Cyclotomic Fields," Springer-Verlag, New York, 1982.
13. 13. G. N. Watson, Theorems stated by Ramanujan (IX): Two continued fractions, J. London Math. Soc. 4 (1929), 231-237.