Orthogonal Polynomials Related to the Oscillatory-chebyshev Weight Function
نویسندگان
چکیده
L(p) = ∫ 1 −1 p(x)x(1− x2)−1/2eiζxdx, ζ ∈ R. Since the weight function alternates in sign in the interval of orthogonality, the existence of orthogonal polynomials is not assured. A nonconstructive proof of the existence is given. The three-term recurrence relation for such polynomials is investigated and the asymptotic formulae for recursion coefficients are derived. AMS Mathematics Subject Classification (2000): Primary 30C10, 33C47
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