Results 41 to 50 of about 1,452,959 (130)
Modular equations for cubes of the Rogers–Ramanujan and Ramanujan–Göllnitz–Gordon functions and their associated continued fractions [PDF]
, 2012 In this paper, we prove modular identities involving cubes of the Rogers–Ramanujan functions. Applications are given to proving relations for the Rogers–Ramanujan continued fraction. Some of our identities are new.
Gugg, Chadwick
core +1 more source
Product formulas for the 5-division points on the Tate normal form and the Rogers–Ramanujan continued fraction [PDF]
Journal of Number Theory, 2016 Explicit formulas are proved for the 5-torsion points on the Tate normal form E 5 of an elliptic curve having ( X , Y ) = ( 0 , 0 ) as a point of order 5. These formulas express the coordinates of points in E 5 [ 5 ] − 〈 ( 0 , 0 ) 〉 as products of linear
Patrick Morton
semanticscholar +1 more source
Exact transient solution of a state‐dependent birth‐death process
International Journal of Stochastic Analysis, Volume 2006, Issue 1, 2006., 2006 A power series expression in closed form for the transient probabilities of a state‐dependent birth‐death process is presented with suitable illustrations.
P. R. Parthasarathy, R. Sudhesh
wiley +1 more source
Another simple proof of the quintuple product identity
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 15, Page 2511-2515, 2005., 2005 We give a simple proof of the well‐known quintuple product identity. The strategy of our proof is similar to a proof of Jacobi (ascribed to him by Enneper) for the triple product identity.
Hei-Chi Chan
wiley +1 more source
Comment on “Some Congruence Properties of a Restricted Bipartition Function cN(n)”
, 2017 International Journal of Analysis, Volume 2017, Issue 1, 2017.
Qing Zou, Ahmed Zayed
wiley +1 more source
A Gauss‐Kuzmin‐Lévy theorem for a certain continued fraction
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 20, Page 1067-1076, 2004., 2004 We consider an interval map which is a generalization of the well‐known Gauss transformation. In particular, we prove a result concerning the asymptotic behavior of the distribution functions of this map.
Hei-Chi Chan
wiley +1 more source
New Enumerations for l-Regular Bipartitions Under Modulo 2 and 3
Journal of MathematicsFor any positive integer l, Bln represents the number of l-regular bipartitions. By employing q-identities, modular equations, and Rogers–Ramanujan continued fraction identities, we establish new congruences under modulo 2 and 3.
null Maheshagouda, B. R. Srivatsa Kumar
doaj +1 more source
Tiling Models for Palindromic and n‐Colored Compositions With 1 s and 3 s
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this work, we explore compositions of positive integers into parts consisting of 1 and 3 s, highlighting their close connection to the Narayana numbers. We also examine palindromic compositions of this type and introduce arithmetic functions that reflect their structural properties.
Orhan Dişkaya +5 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 10, Issue 4, Page 625-640, 1987., 1987 This centennial tribute commemorates Ramanujan the Mathematician and Ramanujan the Man. A brief account of his life, career, and remarkable mathematical contributions is given to describe the gifted talent of Srinivasa Ramanujan. As an example of his creativity in mathematics, some of his work on the theory of partition of numbers has been presented ...
Lokenath Debnath
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Partitions in real quadratic fields
Mathematische Nachrichten, Volume 298, Issue 2, Page 548-566, February 2025.Abstract We study partitions of totally positive integers in real quadratic fields. We develop an algorithm for computing the number of partitions, prove a result about the parity of the partition function, and characterize the quadratic fields such that there exists an element with exactly 1–5, 7, and 11 partitions.
David Stern, Mikuláš Zindulka
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