Bifurcating Continued Fractions
Ashok Kumar Gupta, Ashok Kumar Mittal
Abstract
The notion of 'bifurcating continued fractions' is introduced. Two coupled sequences of non-negative integers are obtained from an ordered pair of positive real numbers in a manner that generalizes the notion of continued fractions. These sequences enable simple representations of roots of cubic equations. In particular, remarkably simple and elegant 'bifurcating continued fraction' representations of Tribonacci and Moore numbers, the cubic variations of the 'golden mean', are obtained. This is further generalized to associate m non-negative integer sequences with a set of m given real numbers so as to provide simple 'bifurcating continued fraction' representation of roots of polynomial equations of degree m+1.
Create a lesson
Related papers
On the Rank Condition for Perfect Cuboids
Valery Asiryan
A Local Proof of Langlands's First Main Lemma for Local Epsilon Factors over Nonarchimedean Local Fields
Fukuhiro Ueda
The first type of power mean bounds for the Gaussian hypergeometric function
Zhen-Hang, Yang, Jing-Feng Tian
On a new class of q-fractional integral operators involving multivariate q-Mittag-Leffler functions
Min-Jie Luo, Qing-Hui Peng, Ravinder Krishna Raina
Partition-theoretic density formulas: radial Tauberian theory and non-radial instability
Mohammad F. Marashdeh
Octonionic Kittaneh Numerical Radius Inequalities
K. Mahesh Krishna