CECM Colloquium, November 12. K9509 at 3.30

Speaker: Jonathan Borwein, Shrum Professor of Science, FRSC, Director CECM, Simon Fraser University

Title: Three adventures: symbolically discovered identities for Zeta(4n+3) and like matters

Abstract: I will describe three sets of results in which computer search and computer algebra played a large role in the discovery/and or proof of results - each ultimately relating to hypergeometric functions.

Apery: A generating function for $\zeta(4n+3)$.

Ramanujan: Integrals, means and transformations of the hypergeometric $\,_2F_1(1/3,2/3,1;1-x^3)$.

Euler: Multivalued $\zeta$--function values and a product of hypergeometric $\,_2F_1$'s.

In each case, my emphasis is on the role of disciplined experimentation and computation.