On generalized hyperharmonic numbers of order r,Hr n,m (σ)

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Atıf İçin Kopyala

KOPARAL S., ÖMÜR N., Elkhiri L.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.29, sa.4, ss.804-812, 2023 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 29 Sayı: 4
• Basım Tarihi: 2023
• Doi Numarası: 10.7546/nntdm.2023.29.4.804-812
• Dergi Adı: NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
• Sayfa Sayıları: ss.804-812
• Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this paper, we define generalized hyperharmonic numbers of order r, H-n,m(r) (sigma), for m is an element of Z(+) and give some applications by using generating functions of these numbers. For example, for n, r, s is an element of Z(+) such that 1 <= s <= r, Sigma(n)(k=1) [GRAPHICS] H-k,m(r-s) (sigma) = H-n,m(r) (sigma), and Sigma(n)(k=1) Sigma(k)(i=1) H-k-i,m(r+1) (sigma) D-r (k - i + r)/(n - k)! (k - i + r)! = H-n,m(2r+2) (sigma), where D-r (n) is an r-derangement number.