45 citations · 114 across the 16 of their papers we have counts for
17 papers
Combinatorics of Continuants of Continued Fractions with 3 Limits
Douglas Bowman, Herman D. Schaumburg
We give combinatorial descriptions of the terms occurring in continuants of general continued fractions that diverge to three limits. Equating these with the usual combinatorial de…
Continued Fraction Proofs of -versions of Some Identities of Rogers-Ramanujan-Slater Type
Douglas Bowman, James Mc Laughlin, Nancy J. Wyshinski
We derive two general transformations for certain basic hypergeometric series from the recurrence formulae for the partial numerators and denominators of two -continued fraction…
Continued Fractions and Generalizations with Many Limits: A Survey
Douglas Bowman, James Mc Laughlin
There are infinite processes (matrix products, continued fractions, -matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge bu…
A -continued fraction
Douglas Bowman, James Mc Laughlin, Nancy J. Wyshinski
We use the method of generating functions to find the limit of a -continued fraction, with 4 parameters, as a ratio of certain -series. We then use this result to give new pr…
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…