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Formulas for Approximate Calculation of the Chebyshev Coefficients

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Abstract

The approximate calculation of integrals is a common part of research in various fields of mathematics, primarily in the theory of approximations and computational mathematics.

In its turn, within the theory of numerical integration, distinctions take place depending on the features of the integrand, the scale of which is “Quadrature (cubature) formulas” and “Theory of oscillations”.

This article belongs to the second type of problems and consists in the approximate calculation of the Chebyshev coefficients.

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REFERENCES

  1. Manin, Yu.I. Mathematics as metaphor (MCCME, Moscow, 2008) [in Russian].

  2. Khavin, V.P. Foundations of calculus (Izd-vo Leningrad. univ., Leningrad, 1989) [in Russian].

  3. Nikolsky, S.M. Quadrature formulas (Nauka, Moscow, 1988) [in Russian].

  4. Bakhvalov, N.S., Zhidkov, N.P., Kobel'kov, G.M. Numerical methods (Nauka, Moscow, 1987) [in Russian].

  5. Babenko, K.I. Foundations of numerical analysis (Nauka, Moscow, 1986) [in Russian].

  6. Korobkov, N.M. Theoretical and numerical methods in approximation analysis (Fizmatgiz, Moscow, 1963) [in Russian].

  7. Hua Loo Keng, Wang Yuan Application of Number Theory of Numerical Analysis (Springer-Verlag, Berlin–Heidelberg–New York, 1981).

  8. Nurmoldin, Y.Y. “Restoration of functions, integrals, and solutions to the heat conductivity equation from the Ulyanov U2-classes”, Siberian J. Numer. Math. 8 (4), 337–351 (2005).

  9. Temirgaliev, N., Kudaibergenov, S.S., Shomanova, A.A. “An application of tensor products of functionals in problems of numerical integration”, Izvestiya: Mathematics 73 (2), 393–434 (2009).

  10. Temirgaliev, N. “Application of the divisors theory to numerical integration of periodic functions in several variables”, Math. USSR-Sb. 69 (2), 527–542 (1990).

  11. Zhubanisheva, A.Z., Temirgalieva, Z.N., Temirgaliev, N. “Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas”, J. Comput. Math. Math. Phys. 49 (1), 12–22 (2009).

  12. Filon, L.N.G. “On a quadrature formula for trigonometric integrals”, Proc. Roy. Soc. Edinburgh 49, 38–47 (1928).

  13. Il'in, A.M., Danilin, A.R. Asymptotic methods in analysis (Fizmatlit, Moscow, 2009) [in Russian].

  14. Zhileykin, Ya.M., Kukarkin, A.B. “Optimal calculation of integrals of highly oscillatory functions”, J. Comput. Math. Math. Phys. 18 (2), 294–301 (1978).

  15. Iserles, A. “On the numerical quadrature of highly-oscillatory integrals II: Irregular oscillators”, IMA J. Num. Anal. 25, 25–44 (2005).

  16. Levin, D. “Procedures for computing one-and-two dimensional integrals of functions with rapid irregular oscillations”, Math. Comp. 38, 531–538 (1982).

  17. Temirgaliyev, N., Kudaibergenov, S.S., Nauryzbayev, N.Zh. “Orderly Exact Calculation of Integrals of Products of Functions by the Method of Tensor Products of Functionals”, Russ. Math. 63 (11), 83–87 (2019).

  18. Suetin, P.K. Classical orthogonal polynomials (Fizmatlit, Moscow, 2005) [in Russian].

  19. Whittaker, E.T., Watson, J.N. A Course of Modern Analysis. P. 2. Transcendental functions (Fizmatlit, Moscow, 1963) [in Russian].

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Funding

This work is funded by the Ministry of Education and Science of the Republic of Kazakhstan (project AP05132938).

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Correspondence to S. S. Kudaibergenov, Y. Y. Nurmoldin, N. Zh. Nauryzbayev or N. Temirgaliyev.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 2, pp. 79–85.

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Kudaibergenov, S.S., Nurmoldin, Y.Y., Nauryzbayev, N.Z. et al. Formulas for Approximate Calculation of the Chebyshev Coefficients. Russ Math. 65, 69–74 (2021). https://doi.org/10.3103/S1066369X21020079

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  • DOI: https://doi.org/10.3103/S1066369X21020079

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