We study the possibility of application of Faber polynomials in proving some combinatorial identities. It is shown that the coefficients of Faber polynomials of mutually inverse conformal mappings generate a pair of mutually invertible relations. We prove two identities relating the coefficients of Faber polynomials and the coefficients of Laurent expansions of the corresponding conformal mappings. Some examples are presented.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 2, pp. 151–164, February, 2018.
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Abdullaev, F.G., Imash-kyzy, M. & Savchuk, V.V. Application of Faber Polynomials in Proving Combinatorial Identities. Ukr Math J 70, 165–181 (2018). https://doi.org/10.1007/s11253-018-1493-0
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DOI: https://doi.org/10.1007/s11253-018-1493-0