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Factorizations that Involve Ramanujan's Function k(q) = r(q)r2(q2)

Factorizations that Involve Ramanujan's Function k(q) = r(q)r2(q2)
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摘要 In the "lost notebook", Ramanujan recorded infinite product expansions for where r -= r(q) is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan's function k = k(q) = r(q)r2 (q2). In the "lost notebook", Ramanujan recorded infinite product expansions for where r -= r(q) is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan's function k = k(q) = r(q)r2 (q2).
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第12期2301-2308,共8页 数学学报(英文版)
关键词 Infinite product Rogers-Ramanujan continued fraction Jacobi triple product identity Infinite product, Rogers-Ramanujan continued fraction, Jacobi triple product identity
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参考文献14

  • 1Ramanujan, S.: The lost notebook and other unpublished papers, Narosa, New Delhi, 1988.
  • 2Berndt, B. C., Huang, S.-S., Sohn, J., et al.: Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan's lost notebook. Trans. Amer. Math. Soc., 352, 2157-2177 (2000).
  • 3Andrews, C. E., Berndt, B. C.: Ramanujan's Lost Notebook, Part I, Springer, New York, 2005.
  • 4Liu, Z.-G.: A theta function identity and the Eisenstein series on Fo(5). J. Ramanujan Math. Soc., 22 283-298 (2007).
  • 5Chan, H.-C., Ebbing, S.: Factorization theorems for the Rogers-Ramanujan continued fraction in the lost notebook. Preprint (Oct. 8, 2008), https://edocs.uis.edu/hchanl/www/.
  • 6Chan, H. H., Chan, S. H., Liu, Z.-G.: The Rogers-Ramanujan continued fraction and a new Eisenstein series identity. Journal of Number Theory, 129, 1786-1797 (2009).
  • 7Ramanujan, S.: Notebooks (2 volumes), Tata Institute of Fundamental Research, Bombay, 1957.
  • 8Berndt, B. C.: Ramanujan's Notebooks, Part V, Springer-Verlag, New York, 1998.
  • 9Cooper, S.: On Ramanujan's function k(q) = r(q)r2(q2). Ramanujan J., 20, 311-328 (2009).
  • 10Cooper, S., Lam, H. Y.: Eisenstein series and elliptic functions on F0(10). Adv. in Appl. Math., 46, 192-208 (2011).

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