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REPRESENTATIONS OF RAMANUJAN CONTINUED FRACTION IN TERMS OF COMBINATORIAL PARTITION IDENTITIES

  • Chaudhary, Mahendra Pal (Department of Mathematics, International Scientific Research and Welfare Organization) ;
  • Choi, Junesang (Department of Mathematics, Dongguk University)
  • Received : 2016.01.18
  • Accepted : 2016.02.18
  • Published : 2016.06.25

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

References

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  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. https://doi.org/10.1016/j.jcta.2014.12.004
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  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.