Some Identities with Special Numbers

Author:

ÖMÜR Neşe1ORCID,SÜDEMEN Kübra Nur1,KOPARAL Sibel2ORCID

Affiliation:

1. KOCAELI UNIVERSITY

2. ULUDAG UNIVERSITY

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

Publisher

Cumhuriyet University

Subject

General Medicine

Reference13 articles.

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).

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