Orthogonal polynomials and some applications, including some
determinants and combinatorial results.
by Richard ASKEY (U.Wisconsin-Madison)
Abstract:
Sylvester stated the value of the tridiagonal determinant
which has
x on the main diagonal,
1,2,...,N above the main diagonal and
N,N-1,...,1 below the main diagonal.
Mark Kac rediscovered this
in a paper which has orthogonal polynomials all over the paper, but
he did not realize this.
Some of the background about orthogonal polynomials will be given and some
applictions will be outlined or summarized. Sylvester's determinant will be
one, and an identity found by Rogers and rediscovered by Ramanujan and Schur
will also be mentioned.
This talk will be accessible to advanced undergraduates as well
as graduate students.