Algorithmic Methods for Special Functions by Computer Algebra
This is a now formally ended postdoc project (November 1999 until
October 2001) which was sponsored by
NWO, gebied Exacte Wetenschappen (project 613-06-565), was
Tom Koornwinder (KdV Institute,
Universiteit van Amsterdam) and
Nico Temme (CWI, Amsterdam),
and was performed by
Raimundas Vidunas, at present working at
National Kapodistrian University of Athens, Greece.
Papers and software produced in the project
A generalization of Kummer's identity by R. Vidunas,
Rocky Mountain J. Math. 32 (2002), 919-936;
An accompanying Maple worksheet
by R. Vidunas joint with T.H. Koornwinder, 2000.
infhsum.mpl (version 4.29, 30 November 2005)
for extension of Zeilberger's algorithm to nonterminating series
(by R. Vidunas).
There is an
accompanying Maple worksheet
by R. Vidunas.
The procedure and worksheets call
W. Koepf's hsum9.mpl.
This material has been tested in Maple 7, 8 and 9.
Symbolic evaluation of coefficients in
Airy-type asymptotic expansions by R. Vidunas and N.M. Temme,
J. Math. Anal. Appl. 269 (2002), 317-331;
By the same authors:
an accompanying Maple package
(version 3.0, 17 January 2001)
and a Maple worksheet
demonstrating the usage of the package.
Contiguous relations of hypergeometric series by R. Vidunas,
J. Comput. Appl. Math. 153 (2003), 507-519;
arXiv:math.CA/0109222 v4 corrects formulas (24) and (25) in that journal
See also an accompanying Maple package
contiguous2f1.mpl and a Maple worksheet
the usage of this package,
Parabolic cylinder functions: examples of error bounds for
asymptotic expansions by N.M. Temme and R. Vidunas,
Anal. Appl. (Singap.) 1 (2003), 265-288;
Transformations of some Gauss hypergeometric functions
by R. Vidunas,
J. Comput. Appl. Math. 178 (2005), 473-487;
Uniform convergence of hypergeometric series
by R. Vidunas,
Related papers and software produced outside the project
1to Tom Koornwinder's home page