Apéry-Like Formulae for $\zeta(4n+3)$

Abstract. Last year, Jon Borwein and I discovered some new series acceleration formulae for integral values of the Riemann zeta function. Apart from their intrinsic beauty, these formulae are interesting because a special instance featured in Apéry's proof of the irrationality of $\zeta(3).$ Some of these formulae have been classified and connected with strange hypergeometric series evaluations, but much work remains to be done. In this talk, I will give an introduction to this exciting area of research, and discuss the role that inverse symbolic computation played in the discovery process.