Seminar Details

In this seminar, we will provide a brief introduction to the early history of series with sums of 1/π and 1/π2, we meet Ramanujan, and discuss the role played by the recently deceased Jesus Guillera in this story. We derive closed-form expressions for values of generalized hypergeometric functions that elegantly combine Ramanujan's series and Guillera's series, as well as others that combine Guillera's series with the series with sum 1/π4. For this we use Zeilberger's algorithm. A side result of the method used is a new (?) series for the constant G/π3, that Jesus Guillera probably would have liked, G being Catalan's constant.

[Joint work with John Campbell]