Results 31 to 40 of about 1,452,959 (130)
On the complete solution of the general quintic using Rogers-Ramanujan continued fraction [PDF]
, 2022 In this article we give solution of the general quintic equation by means of the Rogers-Ramanujan continued fraction. More precisely we express a root of the quintic as a known algebraic function of the Rogers-Ramanujan continued fraction.Comment ...
Bagis, Nikos
core
Some Congruence Properties of a Restricted Bipartition Function cN(n)
International Journal of Analysis, Volume 2016, Issue 1, 2016., 2016 Let cN(n) denote the number of bipartitions (λ, μ) of a positive integer n subject to the restriction that each part of μ is divisible by N. In this paper, we prove some congruence properties of the function cN(n) for N = 7, 11, and 5l, for any integer l≥1, by employing Ramanujan’s theta‐function identities.
Nipen Saikia +2 more
wiley +1 more source
Variations on a result of Bressoud [PDF]
, 2013 The well-known Rogers-Ramanujan identities have been a rich source of mathematical study over the last fifty years. In particular, Gordon’s generalization in the early 1960s led to additional work by Andrews and Bressoud in subsequent years ...
Kurşungöz, Kağan, Sellers, James A.
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Journal of Numbers, Volume 2014, Issue 1, 2014., 2014 We prove general theorems for the explicit evaluations of the level 13 analogue of Rogers‐Ramanujan continued fraction and find some new explicit values. This work is a sequel to some recent works of S. Cooper and D. Ye.
Nipen Saikia, Cheon S. Ryoo
wiley +1 more source
Continued Fractions of Order Six and New Eisenstein Series Identities
Journal of Numbers, Volume 2014, Issue 1, 2014., 2014 We prove two identities for Ramanujan’s cubic continued fraction and a continued fraction of Ramanujan, which are analogues of Ramanujan’s identities for the Rogers‐Ramanujan continued fraction. We further derive Eisenstein series identities associated with Ramanujan’s cubic continued fraction and Ramanujan’s continued fraction of order six.
Chandrashekar Adiga +3 more
wiley +1 more source
Modular Identities and Explicit Evaluations of a Continued Fraction of Ramanujan
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We study a new continued fraction of Ramanujan. We prove its modular identities and give some explicit evaluations.
Nipen Saikia, Stefaan Caenepeel
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A Parameter for Ramanujan′s Function χ(q): Its Explicit Values and Applications
International Scholarly Research Notices, Volume 2012, Issue 1, 2012., 2012 We define a new parameter Ik,n involving quotient of Ramanujan′s function χ(q) for positive real numbers k and n and study its several properties. We prove some general theorems for the explicit evaluations of the parameter Ik,n and find many explicit values.
Nipen Saikia +3 more
wiley +1 more source
The Rogers--Ramanujan continued fraction and related Eta-Quotient representations
, 2021 We construct eta-quotient representations of two families of $q$-series involving the Rogers--Ramanujan continued fraction by establishing related recurrence relations.
Tang, D., Chern, S.
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The level 13 analogue of the Rogers–Ramanujan continued fraction and its modularity
, 2016 We prove the modularity of the level 13 analogue r13(τ) of the Rogers–Ramanujan continued fraction. We establish some properties of r13(τ) using the modular function theory. We first prove that r13(τ) is a generator of the function field on Γ0(13).
Yoonjin Lee, Y. Park
semanticscholar +2 more sources
Probabilities as Values of Modular Forms and Continued Fractions
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms. Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers‐Ramanujan and Ramanujan‐ Selberg‐ Gordon‐Göllnitz continued ...
Riad Masri, Ken Ono, Pentti Haukkanen
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