rJacobi.m

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rJacobi.m#

This subroutine generates the first \(n\) recurrence coefficients for monic Jacobi polynomials with parameters \(a\) and \(b\). These polynomials are orthogonal on \([-1, 1]\) relative to the weight function

\[ w(t) = (1 - t)^a (1 + t)^b. \]

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 = rJacobi(n, a) is the same as ab = rJacobi(n, a, a), and
ab = rJacobi(n) is the same as ab = rJacobi(n, 0, 0).

ab=rJacobi(N,a,b)

Inputs#

  • N : The number of quadrature points.

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

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

Outputs#

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

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