9 citations · 28 across the 7 of their papers we have counts for
7 papers
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…
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…
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…
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…
Real Numbers With Polynomial Continued Fraction Expansions
James Mc Laughlin, Nancy J. Wyshinski
In this paper we show how to apply various techniques and theorems (including Pincherle's theorem, an extension of Euler's formula equating infinite series and continued fractions,…
Ramanujan and Extensions and Contractions of Continued Fractions
James Mc Laughlin, Nancy J. Wyshinski
If a continued fraction is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b…
Ramanujan and the Regular Continued Fraction Expansion of Real Numbers
James Mc Laughlin, Nancy J. Wyshinski
In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^…