Displaying similar documents to “On some trigonometric power sums.”

Integrable systems in the plane with center type linear part

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.

Integral presentations of deviations of de la Vallee Poussin right-angled sums

Vladimir I. Rukasov, Olga G. Rovenska (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We investigate approximation properties of de la Vallee Poussin right-angled sums on the classes of periodic functions of several variables with a high smoothness. We obtain integral presentations of deviations of de la Vallee Poussin sums on the classes C β , m α .

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ( 2 ) ) λ ( V ) for any two-dimensional real symmetric space V.

Several Differentiation Formulas of Special Functions. Part VI

Bo Li, Pan Wang (2007)

Formalized Mathematics

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In this article, we prove a series of differentiation identities [3] involving the secant and cosecant functions and specific combinations of special functions including trigonometric, exponential and logarithmic functions.