Modular Relations for the Sextodecic Analogues of the Rogers-Ramanujan Functions with its Applications to Partitions

Adiga Chandrashekar^1, and Nasser Abdo Saeed Bulkhali¹

¹Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore, India

Cite this paper:
Adiga Chandrashekar and Nasser Abdo Saeed Bulkhali. Modular Relations for the Sextodecic Analogues of the Rogers-Ramanujan Functions with its Applications to Partitions. American Journal of Mathematical Analysis. 2014; 2(3):36-44. doi: 10.12691/ajma-2-3-2

Abstract

In his Ph.D. thesis, C. Gugg considered four functions of order 16 that are analogues of the Rogers-Ramanujan functions and established 12 modular relations involving these functions. In this paper, we obtain 16 new modular relations for these functions. Furthermore, we give partition theoretic interpretations for some of our modular relations.

Keywords:
Rogers-Ramanujan functions theta functions partitions colored partitions modular relations

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