Computing Bernoulli and Tangent numbers

  • warning: Parameter 1 to drutex_pdf_nodeapi() expected to be a reference, value given in /irmacs/drupal/drupal-6x/sites/jonfest2011.irmacs.sfu.ca/modules/drutex/drutex.module on line 829.
  • warning: Parameter 1 to drutex_pdf_nodeapi() expected to be a reference, value given in /irmacs/drupal/drupal-6x/sites/jonfest2011.irmacs.sfu.ca/modules/drutex/drutex.module on line 829.
  • warning: Parameter 1 to drutex_pdf_nodeapi() expected to be a reference, value given in /irmacs/drupal/drupal-6x/sites/jonfest2011.irmacs.sfu.ca/modules/drutex/drutex.module on line 829.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-1 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-2 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-3 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-4 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-5 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-6 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-7 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-8 has been created.
  • The directory /tmp/drutex-b04c8f39a4c1123d89b417370c546ddd-9 has been created.
Speaker: 

Brent, Richard

Affiliation: 
Australian National University

Abstract

TeX Embedding failed! are rational numbers TeX Embedding failed! defined by the generating function

TeX Embedding failed!

They are of interest in number theory and are related to special values of the Riemann zeta function. They also occur as coefficients in the Euler-Maclaurin formula. The closely related TeX Embedding failed! TeX Embedding failed!, defined by

TeX Embedding failed!

are more convenient for computation because they are integers. In this talk I will consider some algorithms for computing Bernoulli and Tangent numbers. In particular, I will give a very simple in-place algorithm for computing the first TeX Embedding failed! Tangent numbers using TeX Embedding failed! integer operations. Although this is not the asymptotically fastest algorithm, it is extremely simple and convenient for moderate values of TeX Embedding failed!.

Video: 

Details

Date & Time: 
Tuesday, May 17, 2011 - 16:30 - 17:00
Venue/Room: 
ASB 10900