Systems of derivatives of polynomials, related to Chebyshev polynomials

V.V. Dostojna (Lviv Polytechnic National University)

Abstract


Properties of the derivatives of polynomials of a complex variable that are related to Chebyshev polynomials and conditions of expansion of analytic functions in circle into series by them are investigated. Examples of such expansions are presented.

Keywords


analytic function; Chebyshev polynomials; biorthogonal system of functions; associated function

References


Pashkovskij S. Computing applications of Chebyshev polynomials and series, Nauka, Moscow, 1983; 384 p. (in Russian)

Polya G., Szego G. Problems and theorems in analysis, Nauka, Moscow, 1978; vol. 1: 392 p. (in Russian)

Szego G. Orthogonal polynomials, GIFML, Moscow, 1962; 500 p. (in Russian)

Sukhorol's'kyj M.A. "System of derivatives of Chebyshev polynomials on a complex plane", Metoda matematyky, 2008; 6: pp. 8-15. (in Ukrainian)

Sukhorol's'kyj M.A. "Approximation of functions by Legendre polynomials on a complex area", Visn. nats. un-tu "L'vіvs'ka polіtekhnіka". Ser.: Fiz.-mat. nauky, 2009; 643: pp. 3-14. (in Ukrainian)

Sukhorol's'kyj M.A., Dostojna V.V. "Expansion of functions, analytical in a circle, on a complex area, by the system of derivatives of Legendre polynomials", Visn. nats. un-tu "L'vіvs'ka polіtekhnіka". Ser.: Fiz.-mat. nauky, 2010; 687: pp. 105-121. (in Ukrainian)

Markushevich A.I. Selected chapters of the theory of analytical functions, Nauka, Moscow, 1976; 192 p. (in Russian)

Bateman H., Erdeji A. Higher transcendental functions, Nauka, Moscow, 1974; vol. 2: 296 p. (in Russian)

Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and series. Elementary functions, Nauka, Moscow, 1981; 800 p. (in Russian)

Bateman H., Erdeji A. Higher transcendental functions, Nauka, Moscow, 1973; vol. 1: 294 p. (in Russian)

Zheverzheev V.F., Kal'nitskij L.A., Sapogov N.A. Special course in higher mathematics for VTUZes, Vyssh. shk., Moscow, 1970; 416 p. (in Russian)

Stein I., Weiss G. Introduction to Fourier analysis on Euclidean spaces, Mir, Moscow, 1974; 336 p. (in Russian)




DOI: https://dx.doi.org/10.15421/241504

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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