125 Alta Jooste
125 Alta Jooste
Recurrence equations involving orthogonal polynomials with related weight functions
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Abstract:
Every sequence of real polynomials {p_n}_{n=0}^\infty=0, orthogonal with respect to a positive weight function w(x) on the interval (a,b), satisfies a three-term recurrence equation. We discuss the role played by the polynomials associated to p_n, especially as coefficient polynomials in the three-term recurrence equation involving polynomials p_n, p_{n-1} and p_{n-m}, m in {2,3,...,n-1}. Furthermore, we show how Christoffel's formula is used to obtain mixed three-term recurrence equations involving the polynomials p_n, p_{n-1} and g_{n-m,k}, m in {2,3,...,n-1}, where the sequence {g_{n,k}}_{n=0}^\infty, k in N_0, is orthogonal with respect to c_k(x)w(x) > 0 on (a,b) and c_k is a polynomial of degree k in x. We discuss the conditions on k, necessary and sufficient for these equations to be in such a form, that they can be applied in the study of the location of the zeros of the
Rod Halburd | |
21 | |
5/14/2024 | |
00:38:08 | |
CAvid, Complex Analysis, Orthogonal Polynomials |