TY - JOUR AU - kyzy M. Imash AU - F. G. Abdullayev AU - V. V. Savchuk PY - 2018/02/25 Y2 - 2024/03/29 TI - Application of the Faber polynomials in proving combinatorial identities JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 70 IS - 2 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1547 AB - We study the possibility of application of the Faber polynomials in proving some combinatorial identities. It is shownthat the coefficients of Faber polynomials of mutually inverse conformal mappings generate a pair of mutually invertiblerelations. We prove two identities relating the coefficients of Faber polynomials and the coefficients of Laurent expansionsof the corresponding conformal mappings. Some examples are presented. ER -