Experimental Mathematics
Since the late 1940s when computers were introduced,
they have had a profound impact on every area of
scientific inquiry. While the computer's underpinnings
were developed both pure mathematicians, they have seen
relative little payback to their area. This has been
dramatically changing since the advent of symbolic computation
packages such as Maple and Mathematica.
These systems have matured to a point
where they are used by researchers not only for disposing of
rote calculations, but as allies in the discovery process.
One now can use the computer to discover new mathematical
patterns and relationships, create impressive graphics
to expose mathematical structure, falsify conjectures,
confirm analytically derived results, and  perhaps most
impressively for the purist  suggest approaches for formal
proofs. This is the thrust of experimental mathematics.
It is a growing paradigm which
is revolutionizing how some
mathematical research is being done today.
My papers which have used the computer to discover new results
follow.
Accepted
Published

M. Chamberland, P. Lopatto,
(2011),
Formulas for Odd Zeta Values and Powers of Pi
,
Journal of Integer Sequences
14 , article 11.2.5, 15.

M. Chamberland, A. Gasull(2010),
Chini equations and isochronous centers
in three dimensional differential systems
,
Qualitative Theory of Dynamical Systems.
9, 2938.

M. Chamberland, K. Dilcher (2009),
A binomial sum related to Wolstenholme's theorem
,
Journal of Number Theory.
129, 26592672.

M. Chamberland (2009),
Ramanujan's 6810 Equation and Beyond
,
Mathematics Magazine.
82, 135140.

M. Chamberland (2008),
Using Integer Relations Algorithms for finding Relationships among Functions
,
Contemporary Mathematics,
457
,(2008),
127133,
"Tapas in Experimental Mathematics",
AMS Special Session on Experimental Mathematics,
January 5, 2007, New Orleans, LA, T. Amdeberhan and
V. Moll editors.

M. Chamberland, M. Martelli (2007),
The MeanMedian Map,
Journal of Difference Equations and Applications
13, 577583.

J. Borwein, M. Chamberland (2007),
Integer Powers of Arcsin
,
International Journal of Mathematics and Mathematical Sciences

M. Chamberland, C. French,
(2006),
Generalized Catalan Numbers and Generalized Hankel Transformations
,
Journal of Integer Sequences
10 , article 07.1.1, 17.

M. Chamberland and Karl Dilcher, (2006),
Divisibility Properties of a Class of Binomial Sums
,
Journal of Number Theory,
120, 349371.

M. Chamberland and Victor H. Moll, (2006),
Dynamics of the degree six Landen
Transformation,
Discrete and Continuous Dynamical Systems,
15, 905919.

M. Chamberland, (2006),
Dynamics of Maps with
Nilpotent Jacobians,
Journal of Difference Equations and Applications,
12, 4956.

M. Chamberland (2003),
Binary BBPFormulas for Logarithms and Generalized Gaussian Mersenne Primes,
Journal of Integer Sequences
6 , article 03.3.7, 110.

M. Chamberland (2003),
Unbounded Ducci Sequences,
Journal of Difference Equations and Applications
9 , 887895

M. Chamberland and M. Martelli (2003),
Unbounded Orbits and Binary Digits,
Journal of Difference Equations and Applications
9 , 687691