gb {midasml}

Gegenbauer polynomials shifted to [a,b]

Description

For a given set of points in X, computes the orthonormal Gegenbauer polynomials basis of L2 [a,b] for a given degree and \alpha parameter. The Gegenbauer polynomials are a special case of more general Jacobi polynomials. In turn, you may get Legendre polynomials from Gegenbauer by setting \alpha = 0, or Chebychev's polynomials by setting \alpha = 1/2 or -1/2.

Usage

gb(degree, alpha, a = 0, b = 1, jmax = NULL, X = NULL)

Arguments

degree

polynomial degree.

alpha

Gegenbauer polynomials parameter.

a

lower shift value (default - 0).

b

upper shift value (default - 1).

jmax

number of high-frequency lags.

X

optional evaluation grid vector.

Value

Psi weight matrix with Gegenbauer functions upto degree.

Author(s)

Jonas Striaukas

Examples

degree <- 3
alpha <- 1
jmax <- 66
gb(degree = degree, alpha = alpha, a = 0, b = 1, jmax = jmax)