Mathematical topics
Don Ramirez
and I collaborated on an algorithm for finding the surface measure of
ellipsoids in N-dimensional space (in fact this evaluates a Lauricella
F-D type function). The algorithm and its derivation appeared in ACM
TOMS 20 (1994), pp. 413-426, 427-435. Click here for the Fortran code
Also the Lauricella F-D is used to compute generalized F-distributions,
(Australian
& New Zealand J. Stat. 43(2001), 21-31) see
math.CA/9906095 .
The abstract of my paper Intertwining
operators and polynomials associated with the symmetric group
. , Monatsh. Math. 126(1998), 181-209 ( there is a gzipped ps
preprint (110K)
). The sequel Intertwining
Operators of Type
B_N , CRM Proceedings and Lecture Notes, vol. 22, 1999, pp.119-134
is here (compressed
ps.gz file, 77K).
An article in J. Symb. Comp 28(1999), 819-826 , the proceedings
of
the ISAAC 1997 session on "Orthogonal Polynomials and Computer
Algebra":
Computing with Differential-Difference Operators"
, (ps, 170k, revised 4/30/98); there is an accompanying Maple V,
Release
4, worksheet
with procedures and examples
.
Algorithms for computing non-symmetric Jack and associated Hermite
polynomials, in the p-basis constructed in Mh. Math. 126(1998) and
Comm. Math. Phys. 197(1998),
451-487, are implemented in the Maple V, Release 4 (easily upgradeable
to
5) worksheet
.
Preprint of "Planar harmonic polynomials of type B"( J. Phys.A:
Math. Gen.
32 (1999), 8095-8110.A) (
math.CA/9906041
), gzip ps
(112kb) .
Preprint of "Generating Functions Associated with Dihedral Groups",
(Nov.
1999) gzip
ps (92 kb)
Note on a strange Laguerre polynomial orthogonality, see arxiv
math-ph/0011021
I participated in the Programme on Macdonald Symmetric Functions, at
the
Newton Institute for
Mathematical
Sciences at Cambridge University, Spring 2001; and was a plenary
lecturer at
the 6th International
Symposium on Orthogonal Polynomials, Special Functions and
Applications, in
Rome, June 2001.
Links
last updated 24 September 2007