doiSerbia

Orthogonal polynomials for the oscillatory-Gegenbauer weight

Milovanović Gradimir V. (Faculty of Computer Sciences, Megatrend University, Beograd)
Cvetković Aleksandar S. (Faculty of Science and Mathematics, Niš)
Marjanović Zvezdan M. (Faculty of Electronic Engineering, Niš)

This is a continuation of our previous investigations on polynomials orthogonal with respect to the linear functional L : P→C, where L = ∫1 -1 p(x) dμ(x), dμ(x) = (1-x²)λ-1/2 exp(iζx) dx, and P is a linear space of all algebraic polynomials. Here, we prove an extension of our previous existence theorem for rational λ ∈ (-1/2,0], give some hypothesis on three-term recurrence coefficients, and derive some differential relations for our orthogonal polynomials, including the second order differential equation.