Application of Faber Polynomials in Proving Combinatorial Identities

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

Ukrainian Mathematical Journal, cilt.70, sa.2, ss.165-181, 2018 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s11253-018-1493-0
  • Dergi Adı: Ukrainian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.165-181
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.