Invariant hyperplanes and Darboux integrability of polynomial vector fields
Journal of Physics A: Mathematical and General, 2002Summary: This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in \(n\) variables. This result generalizes those given by \textit{J. C. Artés, B. Grünbaum} and \textit{J. Llibre} [Pac. J. Math. 184, No.
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A Christoffel-Darboux-Type Formula for Szegö Polynomials and Polynomial Evaluation
1999Polynomials Φ n , n ≥ 0, orthogonal on the complex unit circle satisfy a recurrence relation. If we shift their recurrence coefficients, we obtain the associated polynomials, which can be modified by changing the initialization. We prove a dual recurrence relation and a mixed Christoffel-Darboux-type formula, which expresses the derivative of an ...
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