How to generate unknown orthogonal polynomials out of known orthogonal polynomials

How to generate unknown orthogonal polynomials out of known orthogonal polynomials

We consider the problem of generating the three-term recursion coefficients of orthogonal polynomials for a weight function v(t) = r(t)w(t), obtained by modifying a given weight function w by a rational function r. Algorithms for the construction of the orthogonal polynomials for the new weight v in terms of those for the old weight w axe presented. All the methods are based on modified moments...

Orthogonal Polynomials

The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipl...

Orthogonal Polynomials

Orthogonal Polynomials

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Orthogonal Polynomials with Orthogonal Derivatives