EN
On $ p,q $-Harmonic Numbers
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.
Keywords
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Publication Date
October 31, 2022
Submission Date
September 28, 2022
Acceptance Date
October 31, 2022
Published in Issue
Year 2022 Volume: 10 Number: 2
APA
Halıcı, S., & Gür, Z. B. (2022). On $ p,q $-Harmonic Numbers. Konuralp Journal of Mathematics, 10(2), 375-381. https://izlik.org/JA23UP22SY
AMA
1.Halıcı S, Gür ZB. On $ p,q $-Harmonic Numbers. Konuralp J. Math. 2022;10(2):375-381. https://izlik.org/JA23UP22SY
Chicago
Halıcı, Serpil, and Zehra Betül Gür. 2022. “On $ P,q $-Harmonic Numbers”. Konuralp Journal of Mathematics 10 (2): 375-81. https://izlik.org/JA23UP22SY.
EndNote
Halıcı S, Gür ZB (October 1, 2022) On $ p,q $-Harmonic Numbers. Konuralp Journal of Mathematics 10 2 375–381.
IEEE
[1]S. Halıcı and Z. B. Gür, “On $ p,q $-Harmonic Numbers”, Konuralp J. Math., vol. 10, no. 2, pp. 375–381, Oct. 2022, [Online]. Available: https://izlik.org/JA23UP22SY
ISNAD
Halıcı, Serpil - Gür, Zehra Betül. “On $ P,q $-Harmonic Numbers”. Konuralp Journal of Mathematics 10/2 (October 1, 2022): 375-381. https://izlik.org/JA23UP22SY.
JAMA
1.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, Oct. 2022, pp. 375-81, https://izlik.org/JA23UP22SY.
Vancouver
1.Serpil Halıcı, Zehra Betül Gür. On $ p,q $-Harmonic Numbers. Konuralp J. Math. [Internet]. 2022 Oct. 1;10(2):375-81. Available from: https://izlik.org/JA23UP22SY
