SF Bay Area Talk 25 April - Finding New Mathematical Identities by Supercomputer

[David Hough]

At Stanford:

Tea and Coffee will be available in the common area,
level 3 of Margaret Jacks Hall, at 3:45p.m.


DATE: Monday April 25th 
TIME: 4:15 p.m.
ROOM: 380-380X
SPEAKER:David Bailey 
FROM: NASA Ames 
TITLE: 
Finding New Mathematical Identities by Supercomputer

Abstract:

In response to a letter from Goldbach, Euler considered sums of the
form

  oo
  --- [     1     1     1           1 ]   1
  \   [1 + --- + --- + --- + ... + ---] ------
  /   [      m     m     m           m]      n
  --- [     2     3     4           k ] (k+1)
  k=1

for positive integers m and n.  Euler was able to give explicit values
for certain of these sums in terms of the Riemann zeta function.
Euler's results have now been extended to a significantly larger class
of iterated sums, including sums with alternating signs.  The
resulting formulas involve basic constants such as pi, zeta(n) for
even n, log(2) and others.

This research was facilitated by numerical computations using an
algorithm that can determine, with high confidence, whether or not a
particular numerical value is given by a rational linear combination
of several given constants.  This talk presents the numerical
techniques used in these computations and discusses many of the
experimental and rigorously proven results that have been obtained.

Co-researchers: Jonathan M. Borwein and Roland Girgensohn, Simon
Fraser Univ., Vancouver, BC, Canada