A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F2f . We show how to construct Jacobi forms with various ind...

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

By using the structure theory of Jacobi forms we derive a simple expression for Ozeki polynomials of Type II self-dual binary codes.

This paper centers on the derivation of a Rodrigues-type formula for Gegenbauer matrix polynomial. A connection between Gegenbauer and Jacobi matrix polynomials is given.

The paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so–called Bernstein–Bézier form of a polynomial.

Multiplicative renormalization method (MRM) for deriving generating functions of orthogonal polynomials is introduced by Asai–Kubo– Kuo. They and Namli gave complete lists of MRM-applicable measures for MRM-factors h(x) = ex and (1 − x)−κ. In this paper, MRM-factors h(x) for which the beta distribution B(p, q) over [0, 1] is MRM-applicable are determined. In other words, all generating function...

Consider a root system of type BC1 on the real line R with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an L-space on R to a L-space of C-valued functions on R with the Harish-Chandra measure |c(λ)|dλ. By introducing a weight function of the form cosh(t) tanh t on R we find an orthogonal basis for the L-space on R consisting of even and odd func...

We show that the skew-growth function of a dual Artin monoid of finite type P has exactly rank(P ) =: l simple real zeros on the interval (0, 1]. The proofs for types Al and Bl are based on an unexpected fact that the skewgrowth functions, up to a trivial factor, are expressed by Jacobi polynomials due to a Rodrigues type formula in the theory of orthogonal polynomials. The skew-growth function...

The complexity measures of the Crámer-Rao, Fisher-Shannon and LMC (López-Ruiz, Mancini and Calvet) types of the Rakhmanov probability density ρn(x) = ω(x)p 2 n(x) of the polynomials pn(x) orthogonal with respect to the weight function ω(x), x ∈ (a, b), are used to quantify various two-fold facets of the spreading of the Hermite, Laguerre and Jacobi systems all over their corresponding orthogona...