The special case of [beta] = [alpha] of the Jacobi polynomial
is called Ultraspherical polynomial and is denoted by [P.
On specializing the coefficients A(N,k) suitably, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] yields a number of known polynomials such as Laguerre polynomial, Hermite polynomial, Jacobi polynomial
, Brafman polynomial, Gould and Hopper polynomials and others.
n], [alpha],[beta] > -1, n [member of] N, denote the Jacobi polynomial
of degree n.
2) and writing the result in terms of x = cos [theta] and the orthonormal Jacobi polynomial
n] denotes the Jacobi polynomial
of degree n with the normalization (4.
alpha],[beta]) denotes the orthonormal Jacobi polynomial
of degree n, it follows from (5.
In all cases we show that the orthogonality conditions characterize the Jacobi polynomial
Author Brian George Spencer Doman examines classical orthogonal polynomials and their additional properties, covering hermite polynomials, associated Laguerre polynomials, Legendre polynomials, Chebyshev polynomials, Gegenbauer polynomials, associated Legendre functions, Jacobi polynomials
, and many other related mathematical subjects over twelve chapters and appendices.
7] proposed a computational method based on Jacobi Polynomials
for solving fuzzy linear FDE on interval [0,1].
I, 1826) extended it to Jacobi polynomials
twelve years later.
In this paper by use of shifted Jacobi polynomials
as basis and operational matrix of derivatives , of them we convert these kinds of equations to nonlinear algebraic equations.
Also, in -, we proposed a form of a prototype class of low frequency selective polynomial analogue filter functions, derived in compact explicit form on a simple way by direct application of the modified Christoffel-Darboux formula for classical continual orthonormal Jacobi polynomials