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A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by R. Askey for this system. An electrostatic interpretation for the zeros of a class of para-orthogonal polynomials associated with the biorthogonal system is also considered. [ABSTRACT FROM AUTHOR]

Let μ be a finite positive Borel measure supported on R , L [ f ] = x f ″ + ( α + 1 − x ) f ′ with α > − 1 , or L [ f ] = 1 2 f ″ − x f ′ , and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials { Q n } n > m that satisfy the orthogonality relations ∫ L [ Q n ] ( x ) x k d μ ( x ) = 0 for all 0 ≤ k ≤ n − 1 . We also provide a fluid dynamics model for the zeros of these polynomials. [ABSTRACT FROM AUTHOR]

Abstract: Let be a finite positive Borel measure on , a fixed natural number and , with . We study algebraic and analytic properties of the sequence of monic polynomials that satisfy the orthogonality relations A fluid dynamics model for source points location of a flow of an incompressible fluid with preassigned stagnation points is also considered. [Copyright &y& Elsevier]