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A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

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Abstract

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

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Authors and Affiliations

  1. National University “L’vivs’ka Politekhnika”, Lviv, Ukraine

    Ol’ga V. Veselovska & Veronika V. Dostoina

Authors
  1. Ol’ga V. Veselovska
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  2. Veronika V. Dostoina
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Corresponding author

Correspondence to Ol’ga V. Veselovska.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 2, pp. 256–277 April–June, 2020.

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Veselovska, O.V., Dostoina, V.V. A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable. J Math Sci 249, 786–803 (2020). https://doi.org/10.1007/s10958-020-04973-0

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  • DOI: https://doi.org/10.1007/s10958-020-04973-0

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