Some Fourier series for generalized hypergeometric polynomials
Shah, Manilal (1969)
Portugaliae mathematica
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Shah, Manilal (1969)
Portugaliae mathematica
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Ivanov, Vladimir V., Volokitin, Evgenii P. (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Javier Chavarriga, Jaume Giné (1997)
Publicacions Matemàtiques
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In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.
Javier Chavarriga (1994)
Applicationes Mathematicae
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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.
Gregorac, R.J. (1989)
International Journal of Mathematics and Mathematical Sciences
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H. L. Manocha (1969)
Collectanea Mathematica
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Juan Varona (2006)
Open Mathematics
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We give a short proof to characterize the cases when arccos(√r), the arccosine of the squareroot of a rational number r ∈ [0, 1], is a rational multiple of π: This happens exactly if r is an integer multiple of 1/4. The proof relies on the well-known recurrence relation for the Chebyshev polynomials of the first kind.
Farahmand, K., Li, T. (2010)
International Journal of Stochastic Analysis
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Javier Chavarriga, Jaume Giné (1996)
Publicacions Matemàtiques
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In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.
Volokitin, Evgenii P. (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Wilkins, J.Ernest jun., Souter, Shantay A. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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Kilgore, Theodore (2005)
Journal of Inequalities and Applications [electronic only]
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