24 citations · 188 across the 39 of their papers we have counts for
7 papers · 2 filters
The Convergence Behavior of -Continued Fractions on the Unit Circle
Douglas Bowman, James Mc Laughlin
In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value…
A convergence theorem for continued fractions of the form
James Mc Laughlin, Nancy J. Wyshinski
In this paper we present a convergence theorem for continued fractions of the form . By deriving conditions on the which ensure that the odd and ev…
Combinatorial Identities Deriving From The -th Power Of A $2\Times 2$ Matrix
James Mc Laughlin
In this paper we give a new formula for the -th power of a matrix. More precisely, we prove the following: Let $A= \left ( \begin{matrix} a & b \\ c & d \end{matrix}…
A Theorem on Divergence in the General Sense for Continued Fractions
Douglas Bowman, James Mc Laughlin
If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settle…
On the Divergence in the General Sense of -Continued Fraction on the Unit Circle
Douglas Bowman, James Mc Laughlin
We show, for each -continued fraction in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which diverges in…
Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields
James Mc Laughlin
Finding polynomial solutions to Pell's equation is of interest as such solutions sometimes allow the fundamental units to be determined in an infinite class of real quadratic field…