SOME IDENTITIES FOR GENERALIZED HARMONIC NUMBERS

KOPARAL S., ÖMÜR N., Südemen K.

Matematicki Vesnik, cilt.76, sa.4, ss.288-302, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.57016/mv-blxv3088
  • Dergi Adı: Matematicki Vesnik
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.288-302
  • Anahtar Kelimeler: Daehee numbers, Generalized hyperharmonic numbers of order r, generating function, Stirling numbers of the first kind and the second kind
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this paper, we derive some nonlinear differential equations from generating function of generalized harmonic numbers and give some identities involving generalized harmonic numbers and special numbers by using these differential equations. For example, for any positive integers N, n, r, α and any integer m ≥ 2, S1(n + N, r + 1) n! = n∑ n∑ i∑ j=0 i=0 l=0 z=0 k=0 ()(l∑ r∑ (−1)l−z−i m l − z × S1(N, r − k + 1)S1 (n − i, k) H(z, j − 1, α) where S1 (n, k) is Stirling number of the first kind. i − l + m − 2 i − l) Nj αi j! (n − i)!.