Application of the Faber polynomials in proving combinatorial identities

  • kyzy M. Imash
  • F. G. Abdullayev
  • V. V. Savchuk

Abstract

We study the possibility of application of the 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.
Published
25.02.2018
How to Cite
Imash kyzy M., AbdullayevF. G., and SavchukV. V. “Application of the Faber Polynomials in proving combinatorial Identities”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 2, Feb. 2018, pp. 151-64, http://umj.imath.kiev.ua/index.php/umj/article/view/1547.
Section
Research articles