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.
They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials
One example of operator is the Rodriguez operator operating on holomorphic functions, this is a generalization of the Rodriguez formula for Laguerre and Jacobi polynomials
These include among others, the Leguerre polynomials, the Jacobi polynomials
, the Hermite polynomials, the Brafman polynomials and several others [16, pp.
It is well known that the spectral Tau method based on the classical Jacobi polynomials
(Jacobi Tau method) allows the approximation of infinitely smooth solutions of operator equations such that the truncation error approaches zero faster than any negative power of the number of basis functions used in the approximation as that number tends to [infinity].
Schur functions can be replaced with characters of symplectic group or, more, generally, with multivariate Jacobi polynomials
It is clear that our methods can also be used to deal with the other orthogonal polynomials, such as the Legendre polynomials, the Chebyshev polynomials, Jacobi polynomials
and the Hermite polynomials, etc.
Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
It is worth quoting that an alternative method for the computation of the recurrence coefficients could resort to the more general sub-range Jacobi polynomials
approach studied in .
In this paper, we investigate the extent to which Stieltjes interlacing holds between the zeros of two Jacobi polynomials
if each polynomial belongs to a sequence generated by a different value of the parameter [alpha] and/or [beta].
Also in each figure the ridge and the one-sided Jacobi polynomials
show a faster convergence than the shifted Chebyshev polynomials.