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Dergiler / Konuralp Journal of Mathematics / 2022 / Volume: 10 Issue: 2

On $ p,q $-Harmonic Numbers

Serpil Halıcı(PAMUKKALE ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)0000-0002-8071-0437
Zehra Betül Gür(PAMUKKALE ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)
Sayfa
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Yayın Tarihi
2022-10-31
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, we examined a new generalization of well-known number sequence which is called harmonic numbers.
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Temel Bulgular & Veri:In this study, we examined a new generalization of well-known number sequence which is called harmonic numbers.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:q-calculus · q-analogue · 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.

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Bu Makaleye Atıf Yap

Halıcı, S., Gür, Z. B. (2022). On $ p,q $-Harmonic Numbers. Konuralp Journal of Mathematics, Volume: 10 Issue: 2. https://ajindex.com/articles/1521555

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Kaynakça (15)

  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.