American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2014, 2(3), 36-44
DOI: 10.12691/ajma-2-3-2
Open AccessArticle

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

Adiga Chandrashekar1, and Nasser Abdo Saeed Bulkhali1

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

Pub. Date: July 04, 2014

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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