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On Certain New Modular Relations for the Rogers-Ramanujan type functions of order Twelve

P. S. Guruprasad|K. R. Vasuki
장전수학회 (Jangjeon Mathematical Society)|2010.07|Advanced Studies in Contemporary Mathematics|제20권 제3호|pp. 319-333

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키워드

Theta functionsPartitionsRogers-Ramanujan functionsColored partitions.
주제분류수학

초록

In this paper, we define the Rogers-Ramanujan type functions M(q) and N(q) of order twelve and obtain some modular relations involving these identities, which are analogues to Ramanujan’s well known forty identities for Rogers-Ramanujan functions. Further, we establish certain color partition identities from them.

Abstract

In this paper, we define the Rogers-Ramanujan type functions M(q) and N(q) of order twelve and obtain some modular relations involving these identities, which are analogues to Ramanujan’s well known forty identities for Rogers-Ramanujan functions. Further, we establish certain color partition identities from them.

참고문헌 (23)

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  10. H. B. C. Darling, "Proofs of certain identities and congruences enunicated by S. Ramanujan", Proc. London Math. Soc., (2), 19, pp.350~372 (1921)
  11. H. Göllnitz, "Partitionen mil Differenzenbedingungen", J. Reine Angew. Math., 225, pp.154~190 (1967)
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  19. L. J. Rogers, "Second memoir on the expansion of certain infinite products", Proc. London Math. Soc., 25, pp.318~343 (1894)
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