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Some Identities with Special Numbers

Year 2022, Volume: 43 Issue: 4, 696 - 702, 27.12.2022
https://doi.org/10.17776/csj.1036733

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

References

  • [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.
Year 2022, Volume: 43 Issue: 4, 696 - 702, 27.12.2022
https://doi.org/10.17776/csj.1036733

Abstract

References

  • [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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Neşe Ömür 0000-0002-3972-9910

Kübra Nur Südemen 0000-0003-4695-7855

Sibel Koparal 0000-0001-9574-9652

Publication Date December 27, 2022
Submission Date December 14, 2021
Acceptance Date December 5, 2022
Published in Issue Year 2022Volume: 43 Issue: 4

Cite

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