East Asian mathematical journal

  • 제31권5호
  • /
  • Pages.659-665
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  • 2015
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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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)
  • 투고 : 2015.07.06
  • 심사 : 2015.09.07
  • 발행 : 2015.09.30
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초록

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.

키워드

참고문헌

  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. https://doi.org/10.1016/j.jcta.2014.12.004
  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. https://doi.org/10.1016/j.jnt.2007.03.007
  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. https://doi.org/10.1090/S0002-9939-98-04527-4
  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.

피인용 문헌

  1. REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES vol.38, pp.2, 2016, https://doi.org/10.5831/HMJ.2016.38.2.367
  2. NOTE ON SOME CHARACTER FORMULAS vol.38, pp.4, 2016, https://doi.org/10.5831/HMJ.2016.38.4.809
  3. CERTAIN IDENTITIES ASSOCIATED WITH CHARACTER FORMULAS, CONTINUED FRACTION AND COMBINATORIAL PARTITION IDENTITIES vol.32, pp.5, 2015, https://doi.org/10.7858/eamj.2016.041
  4. TWO IDENTITIES INVOLVING THETA FUNCTIONS vol.33, pp.3, 2015, https://doi.org/10.7858/eamj.2017.021
  5. NOTE ON Q-PRODUCT IDENTITIES AND COMBINATORIAL PARTITION IDENTITIES vol.39, pp.2, 2015, https://doi.org/10.5831/hmj.2017.39.2.267
  6. TWO NEW RELATIONS BETWEEN Q-PRODUCT IDENTITIES, THETA FUNCTION IDENTITIES AND COMBINATORIAL PARTITION IDENTITIES vol.39, pp.3, 2017, https://doi.org/10.5831/hmj.2017.39.3.379
  7. A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity vol.8, pp.6, 2015, https://doi.org/10.3390/math8060918
  8. On relationships between q-product identities and combinatorial partition identities vol.24, pp.1, 2015, https://doi.org/10.5937/matmor2001083c