Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions

Axioms

Chandrashekar Adiga¹ 

关键词: Rogers-Ramanujan functions;    theta functions;    partitions;    colored partitions;    modular relations;   

DOI  :  10.3390/axioms2010020

来源: mdpi

【 摘 要 】

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functionsof order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan’s forty identities for Rogers-Ramanujan functions. Furthermore, we give partition theoretic interpretations of some of our modular relations.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.