24 citations · 188 across the 39 of their papers we have counts for
9 papers · 1 filter
Powers of a matrix and combinatorial identities
James Mc Laughlin, B. Sury
In this article we obtain a general polynomial identity in variables, where is an arbitrary positive integer. We use this identity to give a closed-form expression fo…
Further Combinatorial Identities deriving from the -th power of a matrix
James Mc Laughlin, Nancy J. Wyshinski
In this paper we use a formula for the -th power of a matrix (in terms of the entries in ) to derive various combinatorial identities. Three examples of our re…
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…