Seminars & Colloquia Calendar
Gosper's algorithm and Bell numbers
Robert Dougherty-Bliss, Rutgers University
Date & time: Thursday, 16 February 2023 at 5:00PM - 6:00PM
Abstract: Computers are now very good at evaluating finite sums in closed form. They can do them almost instantly and can often prove that a sum cannot be evaluated in closed form, like the partial sums of k!. Just like in calculus, we can fix summands that don't yield closed forms by multiplying them by a suitable "summation factor." I will show that this idea, applied to sums of falling factorials, produces sequences of polynomials closely related to the Bell numbers.
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]