Year 2022,
Volume: 10 Issue: 2, 375 - 381, 31.10.2022
Serpil Halıcı
,
Zehra Betül Gür
References
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- [9] M.N. Hounkonnou and S. Arjika, (p,q)–deformed Fibonacci and Lucas polynomials: characterization and Fourier integral transforms, arXiv, 2013,
arXiv:1307.2623v1.
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(2022), 712-724.
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- [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.
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On $ p,q $-Harmonic Numbers
Year 2022,
Volume: 10 Issue: 2, 375 - 381, 31.10.2022
Serpil Halıcı
,
Zehra Betül Gür
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.