Number Theory in the Spirit of Ramanujan

“…Two good sources of information about the Rogers-Ramanujan continued fraction are the last chapter of the introductory book by B. C. Berndt [4] and the expository article by W. Duke [13].…”

Section: Some Preliminary Resultsmentioning

confidence: 99%

The Rogers-Ramanujan continued fraction and a quintic iteration for $1/\pi$

Chan

Cooper

Liaw

2007

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…For a detailed historical account of (and for various investigated developments stemming from) the Rogers-Ramanujan continued fraction (1.12) and identities (1.13) and (1.14), the interested reader may refer to the monumental work [3, p. 77 et seq.] (see also [1,4]). The following continued fraction was recalled in [6, p. 5, Eq.…”

Section: P Chaudhary and J Choimentioning

confidence: 99%

Certain Identities Associated With Character Formulas, Continued Fraction and Combinatorial Partition Identities

Chaudhary¹,

Choi²

2016

East Asian mathematical journal

View full text Add to dashboard Cite

Abstract. Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al.[2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.

show abstract

“…In a paragraph before the proofs of (1.7) and (1.8), Andrews [2, p. 26] mentioned that similar identity exists for k = 7, but this identity was not given in [2]. This missing identity, namely, CΦ 7 (q) = 1 (q; q) 7 9) was later published by Kolitsch [23,Lemma 2]. Recently, N.D. Baruah and B.K.…”

Section: Introductionmentioning

confidence: 99%