rLaguerre.m

ab = rLaguerre(n, a) generates the first \(n\) recurrence coefficients for the monic generalized Laguerre polynomials with parameter \(a\). These polynomials are orthogonal on \([0, \infty)\) relative to the weight function

\[ w(t) = t^a e^{-t}. \]

The \(n\) \(\alpha\)-coefficients are stored in the first column, and the \(n\) \(\beta\)-coefficients in the second column of the \(n \times 2\) array ab.

The call ab = rLaguerre(n) is the same as ab = rLaguerre(n, 0).

ab=rLaguerre(N,a)

Inputs

• N : The number of quadrature points.

• a : The power in the above equation, \(a\).

Outputs

ab is an \(n \times 2\) array ab of recurrence coefficients.