On relationships between q-product identities and combinatorial partition identities

A family of theta-function identities based upon Rα,Rβ and Rm-functions related to Jacobi’s triple-product identity

“…The list of citations, which we have included in this article, is believed to be potentially useful for indicating some of the directions for further researches and related developments on the subject-matter which we have dealt with here. In particular, the recent works by Adiga et al (see [1]- [3]), Cao et al [9], Chaudhary et al (see [10] to [16]), Hahn et al [17], and Srivastava et al (see [26], [31]- [33]) are worth mentioning here.…”

“…where (m ∈ N), for multivaraite R-functions, which we shall use for computation of our main results in Section 2. Ever since the year 2015, several new advancements and generalizations of the existing results were made in regard to combinatorial partition-theoretic identities (see, for example, [14] to [15] ; [25] to [27]). In particular, Chaudhary et al generalized several known results on character formulas (see [13]), Ramanujan's modular equations of degrees 3, 7 and 9 (see [10] and [11]), and so on, by using combinatorial partition-theoretic identities.…”

Relations between Rα, Rβ and Rm functions related to Jacobi’s triple-product identity and the family of theta-function identities

“…The list of citations, which we have included in this article, is believed to be potentially useful for indicating some of the directions for further researches and related developments on the subject-matter which we have dealt with here. In particular, the recent works by Cao et al [6], Chaudhary et al (see [8], [19][20][21][22][23]), Hahn et al [24], and Srivastava et al (see [29,31,34,[37][38][39]) are worth mentioning here.…”

“…Ever since the year 2015, several new advancements and generalizations of the existing results were made in regard to combinatorial partition-theoretic identities (see, for example, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and [30][31][32]). In particular, Chaudhary et al generalized several known results on character formulas (see [20]), Roger-Ramanujan type identities (see [17]), Eisenstein series, the Ramanujan-Göllnitz-Gordon continued fraction (see [18]), the 3-dissection property (see [14]), Ramanujan's modular equations of degrees 3, 7 and 9 (see [11,13]), and so on, by using combinatorial partition-theoretic identities.…”