gb function

Gegenbauer polynomials shifted to [a,b]

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.

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.

Returns

Psi weight matrix with Gegenbauer functions upto degree.

Examples

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

Author(s)

Jonas Striaukas