Curious continued fractions
Andrew Hone (University of Kent)
Thursday 22nd October, 2015 16:00-17:00 Maths 522
There are very few transcendental numbers for which the continued fraction expansion is explicitly known. Here we present two new families of continued fractions for Engel series (sums of reciprocals) which arise from integer sequences by generated nonlinear recurrences with the Laurent property, and use the double exponential growth of the sequences to show that the sum of the series is transcendental. If time allows, we will make some remarks about continued fraction expansions in hyperelliptic function fields, and some related discrete integrable systems.