Neşe ÖMÜR, Kübra Nur SÜDEMEN, Sibel KOPARAL

Some Identities with Special Numbers

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:

Harmonic numbers Cauchy numbers of order r, q- Changhee number, Generating functions,

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[1]Gen"c" ̌ev 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.