Some Identities with Special Numbers

Südemen, Kübra Nur; ömür, neşe; koparal, sibel

doi:10.17776/csj.1036733

Some Identities with Special Numbers

Neşe ÖMÜR, (Kocaeli Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)

Kübra Nur SÜDEMEN, (Kocaeli Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Kocaeli, Türkiye)

Sibel KOPARAL (Bursa Uludağ Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, Bursa, Türkiye)

Cumhuriyet Science Journal

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Yıl: 2022 Cilt: 43 Sayı: 4 Sayfa Aralığı: 696 - 702 Metin Dili: İngilizce DOI: 10.17776/csj.1036733 İndeks Tarihi: 09-01-2023

Some Identities with Special Numbers

Öz:

In this paper, we derive new identities which are related to some special numbers and generalized harmonic numbers H_n (α) by using the argument of the generating function given in [3] and comparing the coefficients of the generating functions. Also considering q -numbers involving q -Changhee numbers Chnq and q-Daehee numbers Dnq, some sums are given. For example, for any positive integer n and any positive real number q > 1, whenα= q/(q-1), we have the relationship between generalized harmonic numbers and q -Daehee numbers

Anahtar Kelime: Harmonic numbers Cauchy numbers of order r q- Changhee number Generating functions

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Genčev M., Binomial sums involving harmonic numbers, Math. Slovaca, 61(2) (2011) 215-226.
[2] Liu G., Generating functions and generalized Euler numbers, Proc. Japan Acad., 84(A) (2008) 29-34.
[3] Wang N.L., Li H., Some identities on the higher-order Daehee and Changhee numbers, Pure and Applied Mathematics Journal, 4(5-1) (2015) 33-37.
[4] Kim T., Mansour T., Rim S.-H., Seo J.-J., A note on 𝑞 −Changhee polynomials and numbers, Adv. Studies Theor. Phys., 8(1) (2014) 35-41.
[5] Graham R.L., Knuth D.E., Patashnik O., Concrete Mathematics. 2nd. Edition, Addison-Wesley Publishing Company, (1994).
[6] Kim D.S., Kim T., Lee S.-H., Seo J.-J., Higher−order Daehee numbers and polynomials, International Journal of Mathematical Analysis, 8 (5-6) (2014) 273-283.
[7] Kim T., Lee S.-H., Mansour T., Seo J.-J., A note on 𝑞 −Daehee polynomials and numbers, Adv. Stud. Comtemp. Math., 24(2) (2014) 155-160.
[8] Srivastava H.M., Choi J.-S., Series associated with the zeta and related functions. Dordrecht, Boston and London, Kluwer Acad. Publ., (2001).
[9] Charalambides C.A., Enumerative Combinatorics. Boca Raton, London, New York, Chapman & Hall/CRC , (2002).
[10] Comtet L., Advanced Combinatorics. Reidel, Doredecht, (1974).
[11] Kwon H.I., Jang G.W., Kim T., Some Identities of Derangement Numbers Arising from Differential Equations, Advanced Studies in Contemporary Mathematics, 28(1) (2018) 73-82.
[12] Park J.W., Kwon J., A note on the degenerate high order Daehee polynomials, Appl. Math. Sci., 9 (2015) 4635–4642.
[13] Rim S.-H., Kim T., Pyo S.-S., Identities between harmonic, hyperharmonic and Daehee numbers, J. Inequal. Appl., 2018 (2018) 168.

APA	ömür n, Südemen K, koparal s (2022). Some Identities with Special Numbers. , 696 - 702. 10.17776/csj.1036733
Chicago	ömür neşe,Südemen Kübra Nur,koparal sibel Some Identities with Special Numbers. (2022): 696 - 702. 10.17776/csj.1036733
MLA	ömür neşe,Südemen Kübra Nur,koparal sibel Some Identities with Special Numbers. , 2022, ss.696 - 702. 10.17776/csj.1036733
AMA	ömür n,Südemen K,koparal s Some Identities with Special Numbers. . 2022; 696 - 702. 10.17776/csj.1036733
Vancouver	ömür n,Südemen K,koparal s Some Identities with Special Numbers. . 2022; 696 - 702. 10.17776/csj.1036733
IEEE	ömür n,Südemen K,koparal s "Some Identities with Special Numbers." , ss.696 - 702, 2022. 10.17776/csj.1036733
ISNAD	ömür, neşe vd. "Some Identities with Special Numbers". (2022), 696-702. https://doi.org/10.17776/csj.1036733

APA	ömür n, Südemen K, koparal s (2022). Some Identities with Special Numbers. Cumhuriyet Science Journal, 43(4), 696 - 702. 10.17776/csj.1036733
Chicago	ömür neşe,Südemen Kübra Nur,koparal sibel Some Identities with Special Numbers. Cumhuriyet Science Journal 43, no.4 (2022): 696 - 702. 10.17776/csj.1036733
MLA	ömür neşe,Südemen Kübra Nur,koparal sibel Some Identities with Special Numbers. Cumhuriyet Science Journal, vol.43, no.4, 2022, ss.696 - 702. 10.17776/csj.1036733
AMA	ömür n,Südemen K,koparal s Some Identities with Special Numbers. Cumhuriyet Science Journal. 2022; 43(4): 696 - 702. 10.17776/csj.1036733
Vancouver	ömür n,Südemen K,koparal s Some Identities with Special Numbers. Cumhuriyet Science Journal. 2022; 43(4): 696 - 702. 10.17776/csj.1036733
IEEE	ömür n,Südemen K,koparal s "Some Identities with Special Numbers." Cumhuriyet Science Journal, 43, ss.696 - 702, 2022. 10.17776/csj.1036733
ISNAD	ömür, neşe vd. "Some Identities with Special Numbers". Cumhuriyet Science Journal 43/4 (2022), 696-702. https://doi.org/10.17776/csj.1036733