Combinatorial Identities and Sums for Special Numbers and Polynomials

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ŞİMŞEK Y.

FILOMAT, cilt.32, sa.20, ss.6869-6877, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 20
  • Basım Tarihi: 2018
  • Doi Numarası: 10.2298/fil1820869s
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.6869-6877
  • Anahtar Kelimeler: Euler numbers, Central factorial numbers, Array polynomials, Stirling numbers, Generating functions, Binomial coefficients, Combinatorial sum, EULER
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, by using some families of special numbers and polynomials with their generating functions and functional equations, we derive many new identities and relations related to these numbers and polynomials. These results are associated with well-known numbers and polynomials such as Euler numbers, Stirling numbers of the second kind, central factorial numbers and array polynomials. Furthermore, by using higher-order partial differential equations, we derive some combinatorial sums and identities. Finally, we give two computation algorithms for Euler numbers and central factorial numbers.