Abstract / résuméCUMC / CCEM 2005

Name / nom: David Shirokoff

School / école: University of Toronto

Length / durée: 50 min

Title / titre: Infinite Sums: Barely and Almost Convergent

Abstract / résumé: The development of calculus brings with it both the tools and desire to study infinite series. Given such a series, one seeks to determine the convergence and subsequently, the evaluation. Based upon convergence criteria, I will consider three classes of summations: ones that grow .slowly. to infinity; ones that converge .slowly.; and ones that diverge but may be assigned a value. Series in the slowly divergent category are chosen for their interesting mathematical and physical consequences. Selections made in the slowly convergent class are based on mathematical evaluation techniques. In contrast, the last class sits in a historical context. By loosening the common rigorous definition of convergence, one may assign reasonable values to otherwise divergent sums. I consider several such divergent sums, their values, and the link to analytic continuation.

Prerequisites / choses nécessaires: None listed.



PDF format / format PDF: shirokoff.pdf