A new type of polynomials approximating a continuous or integrable function
L. Hsu (1959)
Studia Mathematica
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L. Hsu (1959)
Studia Mathematica
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Bernard Beauzamy (1990)
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Kurt Mahler (1972)
Acta Arithmetica
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Zdeněk Vostrý (1978)
Kybernetika
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Javier Chavarriga (1995)
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We study the integrability of two-dimensional autonomous systems in the plane of the form , , where Xs(x,y) and Ys(x,y) are homogeneous polynomials of degree s with s≥2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable with coefficients being functions of tan−1(y/x).
A. Kiełbasiński (1964)
Studia Mathematica
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María T. Acosta de Orozco, Javier Gómez-Calderón (1991)
Extracta Mathematicae
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