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Year 2022, Volume: 10 Issue: 2, 375 - 381, 31.10.2022

Abstract

References

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  • [13] V. Kac, P. Cheung, Quantum Calculus, Springer, New York, 2002.
  • [14] V. Sahai and S. Yadav, On models of certain p;q-algebra representations: The Quantum Euclidean algebra ep;q(2), J. Math. Anal. Appl. Vol:338 (2008), 1043-1053.
  • [15] Z.W. Sun, Arithmetic Theory of Harmonic Numbers, Proc. Am. Math. Soc. Vol:140, No.2 (2012), 415-428.

On $ p,q $-Harmonic Numbers

Year 2022, Volume: 10 Issue: 2, 375 - 381, 31.10.2022

Abstract

In this study, we examined a new generalization of well-known number sequence which is called harmonic numbers. We defined p,q-harmonic numbers which is also a generalization of q-harmonic numbers and deduced some properties and identities related to this number sequence by using some combinatorial operations.

References

  • [1] A. Ciavarella, What is q-Calculus?, Course Hero, 2016, 1-6.
  • [2] A. M. Alanazi, A. Ebaid, W.M. Alhawiti and G. Muhiuddin, The falling body problem in quantum calculus, Front. Phys. Vol:8, No.43 (2020).
  • [3] A. Sofo, Quadratic alternating harmonic number sums, J. Number Theory, Vol:154 (2015), 144-159.
  • [4] C. Kızılates¸, N. Tuglu and B. C¸ ekim, On the (p,q)–Chebyshev Polynomials and Related Polynomials, Mathematics. Vol:7, No.2 (2019), 136.
  • [5] C. Kızılates¸ and N. Tuglu, Some Combinatorial Identities of q-Harmonic and q-Hyperharmonic Numbers, Commun. Math. Appl. Vol:6, No.2 (2015), 33-40.
  • [6] I.M. Burban and A.U. Klimyk,p;q-Differentiation, p;q-integration and p;q-hypergeometric functions related to quantum groups, Integral Transforms Spec. Funct. Vol:2 (1994), 15–36.
  • [7] J. Spiess, Some identities involving harmonic numbers, Math. Comput. Vol:55, No.192 (1990), 839-863.
  • [8] M.N. Hounkonnou and J.D. Bukweli Kyemba, R(p,q) calculus: differentiation and integration, SUTJ. Math. Vol:49, No.2 (2013), 145-167.
  • [9] M.N. Hounkonnou and S. Arjika, (p,q)–deformed Fibonacci and Lucas polynomials: characterization and Fourier integral transforms, arXiv, 2013, arXiv:1307.2623v1.
  • [10] N. O¨ mu¨r, Z.B. Gu¨r and S. Koparal, Congruences with q-generalized Catalan numbers and q-harmonic numbers, Hacet. J. Math. Stat. Vol:51, No.3 (2022), 712-724.
  • [11] R. Corcino, On p,q-Binomial Coefficients, Integers, Vol:8 (2008), A29.
  • [12] S, Aracı, U, Duran, M. Ac¸ıkg¨oz and H. M. Srivastava, A certain p;q-derivative operator and associated divided differences, J. Inequal Appl. Vol:301 (2016), 1240-1248.
  • [13] V. Kac, P. Cheung, Quantum Calculus, Springer, New York, 2002.
  • [14] V. Sahai and S. Yadav, On models of certain p;q-algebra representations: The Quantum Euclidean algebra ep;q(2), J. Math. Anal. Appl. Vol:338 (2008), 1043-1053.
  • [15] Z.W. Sun, Arithmetic Theory of Harmonic Numbers, Proc. Am. Math. Soc. Vol:140, No.2 (2012), 415-428.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Serpil Halıcı 0000-0002-8071-0437

Zehra Betül Gür

Publication Date October 31, 2022
Submission Date September 28, 2022
Acceptance Date October 31, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Halıcı, S., & Gür, Z. B. (2022). On $ p,q $-Harmonic Numbers. Konuralp Journal of Mathematics, 10(2), 375-381.
AMA Halıcı S, Gür ZB. On $ p,q $-Harmonic Numbers. Konuralp J. Math. October 2022;10(2):375-381.
Chicago Halıcı, Serpil, and Zehra Betül Gür. “On $ p,q $-Harmonic Numbers”. Konuralp Journal of Mathematics 10, no. 2 (October 2022): 375-81.
EndNote Halıcı S, Gür ZB (October 1, 2022) On $ p,q $-Harmonic Numbers. Konuralp Journal of Mathematics 10 2 375–381.
IEEE S. Halıcı and Z. B. Gür, “On $ p,q $-Harmonic Numbers”, Konuralp J. Math., vol. 10, no. 2, pp. 375–381, 2022.
ISNAD Halıcı, Serpil - Gür, Zehra Betül. “On $ p,q $-Harmonic Numbers”. Konuralp Journal of Mathematics 10/2 (October 2022), 375-381.
JAMA Halıcı S, Gür ZB. On $ p,q $-Harmonic Numbers. Konuralp J. Math. 2022;10:375–381.
MLA Halıcı, Serpil and Zehra Betül Gür. “On $ p,q $-Harmonic Numbers”. Konuralp Journal of Mathematics, vol. 10, no. 2, 2022, pp. 375-81.
Vancouver Halıcı S, Gür ZB. On $ p,q $-Harmonic Numbers. Konuralp J. Math. 2022;10(2):375-81.
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