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REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES
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  • Journal title : Honam Mathematical Journal
  • Volume 38, Issue 2,  2016, pp.367-373
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2016.38.2.367
 Title & Authors
REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES
Chaudhary, Mahendra Pal; Choi, Junesang;
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 Abstract
Adiga and Anitha [1] investigated the Ramanujan`s continued fraction (18) to present many interesting identities. Motivated by this work, by using known formulas, we also investigate the Ramanujan`s continued fraction (18) to give certain relationships between the Ramanujan`s continued fraction and the combinatorial partition identities given by Andrews et al. [3].
 Keywords
Jacobi`s triple product identity;q-product identities;Ramanujan continued fraction;Combinatorial partition identities;
 Language
English
 Cited by
 References
1.
C. Adiga and N. Anitha, A note on a continued fraction of Ramanujan, Bull. Austral. Math. Soc. 70 (2004), 489-497. crossref(new window)

2.
C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Theta functions and q-series (Chapter 16 of Ramanujan's second notebook), Mem. Amer. Math. Soc. 315 (1985), 1-91.

3.
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. crossref(new window)

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B. C. Berndt, Ramanujan's Notebooks, Part III, Springer-Verlag, Berlin, Heidelberg and New York, 1991.

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B. C. Berndt, Number Theory in the Sprit of Ramanujan, Amer. Math. Soc., Providence, Rhode Island, 2006.

6.
M. P. Chaudhary and J. Choi, Note on modular relations for Roger-Ramanujan type identities and representations for Jacobi identities, East Asian Math. J. 31(5) (2015), 659-665. crossref(new window)

7.
H. M. Srivastava and M. P. Chaudhary, Some relationships between q-product identities, combinatorial partition identities and continued-fractions identities, Adv. Stud. Contemporary Math. 25(3) (2015), 265-272.

8.
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.