Orthogonal Polynomials with Respect to Modified Jacobi Weight and Corresponding Quadrature Rules of Gaussian Type

摘要

In this paper we consider polynomials orthogonal with respect to the linear functional (f): P - C,defined on the space of all algebraic polynomials P by (f) [p]=∫1-1 p(x)(1 - x)α-1/2(1 + x)β-1/2 exp(iζx)dx,where α,β ＞ -1/2 are real numbers such that (l) =｜β - α｜ is a positive integer,and ζ ∈ R{0}.We prove the existence of such orthogonal polynomials for some pairs of a and ζ and for all nonnegative integers (l).For such orthogonal polynomials we derive three-term recurrence relations and also some differential-difference relations.For such orthogonal polynomials the corresponding quadrature rules of Gaussian type are considered.Also,some numerical examples are included.