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Derivations and Identities for Chebyshev Polynomials

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Ukrainian Mathematical Journal Aims and scope

We introduce the notion of Chebyshev derivations of the first and second kinds based on the polynomial algebra and the corresponding specific differential operators, find the elements of their kernels, and prove that any element of the kernel of each derivation specifies a polynomial identity for Chebyshev polynomials of both kinds. We deduce several polynomial identities for the Chebyshev polynomials of both kinds, for a partial case of Jacobi polynomials, and for the generalized hypergeometric function.

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Authors and Affiliations

  1. Khmelnytskyi National University, Khmelnytskyi, Ukraine

    L. P. Bedratyuk

  2. Stus Donetsk National University, Vinnytsya, Ukraine

    N. B. Lunio

Authors
  1. L. P. Bedratyuk
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  2. N. B. Lunio
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Corresponding author

Correspondence to N. B. Lunio.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1011–1022, August, 2021. Ukrainian DOI: 10.37863/umzh.v73i8.2380.

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Bedratyuk, L.P., Lunio, N.B. Derivations and Identities for Chebyshev Polynomials. Ukr Math J 73, 1175–1188 (2022). https://doi.org/10.1007/s11253-022-01985-8

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  • DOI: https://doi.org/10.1007/s11253-022-01985-8

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