Research Article

Some Identities with Special Numbers

Volume: 43 Number: 4 December 27, 2022
Cumhuriyet Science Journal Cover
Cumhuriyet Science Journal
PDF Download
EN

Some Identities with Special Numbers

Abstract

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

Keywords

References

  1. [1]Gen"c" ̌ev M., Binomial sums involving harmonic numbers, Math. Slovaca, 61(2) (2011) 215-226.
  2. [2]Liu G., Generating functions and generalized Euler numbers, Proc. Japan Acad., 84(A) (2008) 29-34.
  3. [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. [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. [5]Graham R.L., Knuth D.E., Patashnik O., Concrete Mathematics. 2nd. Edition, Addison-Wesley Publishing Company, (1994).
  6. [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. [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. [8]Srivastava H.M., Choi J.-S., Series associated with the zeta and related functions. Dordrecht, Boston and London, Kluwer Acad. Publ., (2001).

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Kübra Nur Südemen
0000-0003-4695-7855
Türkiye

Publication Date

December 27, 2022

Submission Date

December 14, 2021

Acceptance Date

December 5, 2022

Published in Issue

Year 2022 Volume: 43 Number: 4

DOI

https://doi.org/10.17776/csj.1036733

IZ

https://izlik.org/JA43DZ57FU

Cite

RIS / Bibtex
APA
Ömür, N., Südemen, K. N., & Koparal, S. (2022). Some Identities with Special Numbers. Cumhuriyet Science Journal, 43(4), 696-702. https://doi.org/10.17776/csj.1036733

Cited By

Some Sums Involving Generalized Harmonic and r-Derangement Numbers

Cumhuriyet Science Journal

https://doi.org/10.17776/csj.1365360

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December