1 research outputs found
Generalized Goncarov polynomials
We introduce the sequence of generalized Gon\v{c}arov polynomials, which is a
basis for the solutions to the Gon\v{c}arov interpolation problem with respect
to a delta operator. Explicitly, a generalized Gon\v{c}arov basis is a sequence
of polynomials defined by the biorthogonality relation
for all
, where is a delta operator, a sequence of scalars, and the evaluation
at . We present algebraic and analytic properties of generalized
Gon\v{c}arov polynomials and show that such polynomial sequences provide a
natural algebraic tool for enumerating combinatorial structures with a linear
constraint on their order statistics.Comment: 24 pp., 2 figure