INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7(2) (2007), #A05 FURTHER ANALOGUES OF THE ROGERS-RAMANUJAN FUNCTIONS WITH APPLICATIONS TO PARTITIONS Nayandeep Deka Baruah 1 Department of Mathematical Sciences, Tezpur University, Napaam-784028, Assam, India nayan@tezu.ernet.in Jonali Bora 2 Department of Mathematical Sciences, Tezpur University, Napaam-784028, Assam, India jonali@tezu.ernet.in Received: 12/28/05, Accepted: 7/31/06 Abstract In this paper, we establish several modular relations involving two functions analogous to the Rogers-Ramanujan functions. These relations are analogous to Ramanujan’s famous forty identities for the Rogers-Ramanujan functions. Also, by the notion of colored partitions, we extract partition theoretic interpretations from some of our relations. –Dedicated to Professor Ron Graham 1. Introduction Throughout the paper, we assume |q| < 1 and for positive integers n, we use the standard notation (a; q) n := n-1  j =0 (1 - aq j ) and (a; q) ∞ := ∞  n=0 (1 - aq n ). The famous Rogers-Ramanujan identities ([20], [16], [17, pp. 214–215]) are G(q) := ∞  n=0 q n 2 (q; q) n = 1 (q; q 5 ) ∞ (q 4 ; q 5 ) ∞ (1) 1 Corresponding author 2 Research partially supported by grant SR/FTP/MA-02/2002 from DST, Govt. of India.