An urn model for the Jacobi-Piñeiro polynomials

Assche, Multiple Wilson and Jacobi-Piñeiro polynomials, manuscript

We introduce multiple Wilson polynomials, which give a new example of multiple orthogonal polynomials (Hermite-Padé polynomials) of type II. These polynomials can be written as a Jacobi-Piñeiro transform, which is a generalization of the Jacobi transform for Wilson polynomials, found by T.H. Koornwinder. Here we need to introduce Jacobi and JacobiPiñeiro polynomials with complex parameters. Som...

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Local Estimates for Jacobi Polynomials

It is shown that if α, β ≥ − 12 , then the orthonormal Jacobi polynomials p (α,β) n fulfill the local estimate |p n (t)| ≤ C(α, β) ( √ 1− x+ 1 n ) α+ 2 ( √ 1 + x+ 1 n ) β+ 2 for all t ∈ Un(x) and each x ∈ [−1, 1], where Un(x) are subintervals of [−1, 1] defined by Un(x) = [x− φn(x) n , x+ φn(x) n ]∩[−1, 1] for n ∈ N and x ∈ [−1, 1] with φn(x) = √ 1− x2+ 1 n . Applications of the local estimate ...

The Addition Formula for Jacobi Polynomials

Recently the author derived a Laplace integral representation, a product formula and an addition formula for Jacobi polynomials Ppfi). The results are (1) (2) and (3) * j, ,I " (~0~2 0-f-2 sin2 0 + ir cos #I sin 28)n * ' P$ycos 281) PFycos 282) 2&x + 1) Pgq 1) Pfq 1)-= l/22 qa-p)r(/l+#. . .

Linearization Coefficients for the Jacobi Polynomials

i P (α,β) ni (x) et en déduire une évaluation dans le cas particulier où n1 = n2 + · · ·+ nm. ABSTRACT. — The explicit non-negative representation of the linearization coefficients of the Jacobi polynomials obtained by RAHMAN seems to be difficult to be derived by combinatorial methods. However several combinatorial interpretations can be provided for the integral of the product of Jacobi polyn...