Early in 2005 I discovered a remarkable eta-product identity that was known most probably to a very few people implicitly and even fewer explicitly. In order to state the identity we first define the infinite product h(q) := q (1/24) (1 − q)(1 − q 2)(1 − q 3)(1 − q 4)...
Dedication It is a great pleasure to dedicate this article to Gerry Ladas, who along with Saber Elaydi, made Difference Equations such an active and exciting field. Somos Sequences In the late 1980s, Michael Somos came up with an amazing set of conjectures, featuring non-linear recurrences that always yield integers. The most famous one was Somos-4:… (More)