A continued fraction of order twelve

Naika, M. S. Mahadeva; Dharmendra, B. N.; Shivashankara, K.

doi:10.2478/s11533-008-0031-y

Cited by 18 publications

(6 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We next prove the fifth identity (33). We apply the identity (9) (with the parameter q replaced by −q, −q 3 , q 2 and q 6 ) under the given precondition of (27). We then further use the results (20) and (21).…”

Section: A Set Of Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

et al. 2020

View full text Add to dashboard Cite

The authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity. These theta-function identities depict the inter-relationships that exist among theta-function identities and combinatorial partition-theoretic identities. Here, in this paper, we consider and relate the multivariable R-functions to several interesting q-identities such as (for example) a number of q-product identities and Jacobi’s celebrated triple-product identity. Various recent developments on the subject-matter of this article as well as some of its potential application areas are also briefly indicated. Finally, we choose to further emphasize upon some close connections with combinatorial partition-theoretic identities and present a presumably open problem.

show abstract

Section: A Set Of Main Resultsmentioning

confidence: 99%

“…In this section, we first suggest some possible applications of our findings in Theorem 3 within the context of continued fraction identities. We begin by recalling that Naika et al [27] studied the following continued fraction:…”

Section: Applications Based Upon Ramanujan's Continued-fraction Identitiesmentioning

confidence: 99%

A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity

et al. 2020

View full text Add to dashboard Cite

show abstract

“…has been studied only recently. A continued fraction for h was derived by Mahadeva Naika et al [22], and several modular equations for h have been given in [18,21,22,26]. The signs of the coefficients in the q-series expansions of h and its reciprocal, along with the 2-, 3-, 4-, 6-and 12-dissections, have been studied by Lin [20].…”

Section: Introductionmentioning

confidence: 99%

The Level 12 Analogue of Ramanujan’s Function

Cooper¹,

Ye²

2016

J. Aust. Math. Soc.

View full text Add to dashboard Cite

We provide a comprehensive study of the function $h=h(q)$ defined by $$\begin{eqnarray}h=q\mathop{\prod }_{j=1}^{\infty }\frac{(1-q^{12j-1})(1-q^{12j-11})}{(1-q^{12j-5})(1-q^{12j-7})}\end{eqnarray}$$ and show that it has many properties that are analogues of corresponding results for Ramanujan’s function $k=k(q)$ defined by $$\begin{eqnarray}k=q\mathop{\prod }_{j=1}^{\infty }\frac{(1-q^{10j-1})(1-q^{10j-2})(1-q^{10j-8})(1-q^{10j-9})}{(1-q^{10j-3})(1-q^{10j-4})(1-q^{10j-6})(1-q^{10j-7})}.\end{eqnarray}$$

show abstract

“…and the functions f (a, b) and f (−q) are given in (5) and (10), respectively. For a detailed historical account of (and for various investigated developments stemming from) the Rogers-Ramanujan continued fraction (12) and identities (13) and 14, the interested reader may refer to the monumental work [5, p. 77 et seq.]…”

Section: Introductionmentioning

confidence: 99%