Hypergeometric series and continued fractions
The use of three term relations among contiguous hypergeometric series to obtain evaluations of continued fractions as a ratio of hypergeometric series is a technique which goes back to Gauss. The author discusses this technique and Ramanujan's use of it, and then employs a q-analog to derive Ramanujan's evaluation of the fraction \[ \frac{1}{1+}\frac{aq+\lambda q}{1+}\frac{bq+\lambda q^ 2}{1+}\frac{aq^ 2+\lambda q^ 3}{1+}\frac{bq^ 2+\lambda q^ 4}{1+}...\quad. \]
scientific article; zbMATH DE number 4077319