SOME IDENTITIES FOR GENERALIZED HARMONIC NUMBERS

KOPARAL S., ÖMÜR N., Südemen K.

Matematicki Vesnik, vol.76, no.4, pp.288-302, 2024 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.57016/mv-blxv3088
  • Journal Name: Matematicki Vesnik
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.288-302
  • Keywords: Daehee numbers, Generalized hyperharmonic numbers of order r, generating function, Stirling numbers of the first kind and the second kind
  • Kocaeli University Affiliated: Yes

Abstract

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)!.