Browse > Article
http://dx.doi.org/10.7858/eamj.2015.046

NOTE ON MODULAR RELATIONS FOR THE ROGER-RAMANUJAN TYPE IDENTITIES AND REPRESENTATIONS FOR JACOBIAN IDENTITY  

CHAUDHARY, M.P. (INTERNATIONAL SCIENTIFIC RESEARCH AND WELFARE ORGANIZATION)
CHOI, JUNESANG (DEPARTMENT OF MATHEMATICS, DONGGUK UNIVERSITY)
Publication Information
East Asian mathematical journal / v.31, no.5, 2015 , pp. 659-665 More about this Journal
Abstract
Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.
Keywords
Rogers-Ramanujan function; Ramanujan's theta function; Jacobi's triple product identity; Modular relations; Combinatorial partition identities; q-Product identities;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. E. Andrews, K. Bringman and K. Mahlburg, Double series representations for Schur's partition function and related identities, J. Combin. Theory Ser. A 132 (2015), 102-119.   DOI   ScienceOn
2 N. D. Baruah and J. Bora, Modular relations for the nonic analogues of the Rogers-Ramanujan functions with applications to partitions, J. Number Theory 128 (2008), 175-206.   DOI   ScienceOn
3 B. C. Berndt, Ramanujan's Notebooks, Part III, Springer-Verlag, New York, 1991.
4 M. P. Chaudhary, Generalization of Ramanujan's identities in terms of q-products and continued fractions, Global J. Sci. Frontier Res. Math. Decision Sci. 12(2) (2012), 53-60.
5 M. P. Chaudhary, On q-product identities, Pacific J. Appl. Math. 5(2) (2013), 123-129.
6 J. A. Ewell, A note on a Jacobian identity, Proc. Amer. Math. Soc. 126 (1998), 421-423.   DOI   ScienceOn
7 H. Hahn, Eisentein series, Analogues of the Ragers-Ramanujan function, and Partition identities, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2004.
8 S. Ramanujan, Notebooks, 2 Volumes, Tata Institute of Fundamental Research, Bombay, 1957.
9 A. Selberg, Uber einige arithmetische Identitaten, Avh. Norske Vid.-Akad. Oslo I. Mat.-Naturv. Kl. 8 (1936), 323.
10 H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
11 H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.