Application of Faber Polynomials in Proving Combinatorial Identities

ABDULLAYEV F., Imash-kyzy M., Savchuk V.

Ukrainian Mathematical Journal, vol.70, no.2, pp.165-181, 2018 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s11253-018-1493-0
  • Journal Name: Ukrainian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.165-181
  • Uşak University Affiliated: No

Abstract

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.