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- Hartford Financial Services (United States)11 papers
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4 papers · 1 filter
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…
The Convergence and Divergence of -Continued Fractions outside the Unit Circle
Douglas Bowman, James Mc Laughlin
We consider two classes of -continued fraction whose odd and even parts are limit 1-periodic for , and give theorems which guarantee the convergence of the continued frac…
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…