Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

SOME EXPLICIT PROPERTIES OF (p, q)-ANALOGUE EULER SUM USING (p, q)-SPECIAL POLYNOMIALS

  • KANG, J.Y. (Department of Mathematics Education, Silla University)
  • 투고 : 2019.11.01
  • 심사 : 2020.01.08
  • 발행 : 2020.01.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we discuss some interesting properties of (p, q)-special polynomials and derive various relations. We gain some relations between (p, q)-zeta function and (p, q)-special polynomials by considering (p, q)-analogue Euler sum types. In addition, we derive the relationship between (p, q)-polylogarithm function and (p, q)-special polynomials.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT and Future Planning(No. 2017R1E1A1A03070483).

참고문헌

  1. M. Arik, E. Demircan, T. Turgut, L. Ekinci, M. Mungan, Fibonacci oscillators, Z. Phys. C:particles and Fields 55 (1992), 89-95. https://doi.org/10.1007/BF01558292
  2. G.E. Andrews, R. Askey, R. Roy, Special functions, Cambridge Press, Cambridge, UK, 1999.
  3. G. Brodimas, A. Jannussis, R. Mignani, Two-parameter quantum groups, Universita di Roma Preprint, Nr. 820 (1991).
  4. D. Borwein, J.M. Borwein, R. Girgensohn, Explicit evaluation of Euler sums, Proc. Edinburgh Math. 38 (1995), 277-294. https://doi.org/10.1017/S0013091500019088
  5. R. Chakrabarti, R. Jagannathan, A (p, q)-oscillator realization of two-parameter quantum algebras, J. Phys. A:Math. Gen. 24 (1991), L711. https://doi.org/10.1088/0305-4470/24/1/004
  6. R.B. Corcino, On p, q-Binomial coefficients, Electron. J. Combin. Number Theory 8 (2008), A29.
  7. K. Dilcher, K. H. Pilehrood, T.H. Pilehrood, On q-analogues of double Euler sums, J. Math. Anal. Appl. 410 (2014), 979-988. https://doi.org/10.1016/j.jmaa.2013.09.017
  8. P. Flajolet, B. Salvy, Euler Sums and Contour Integral Representations, Exp. Math. 7 (1998), 15-35. https://doi.org/10.1080/10586458.1998.10504356
  9. N.I. Mahmudov, A Akkeles, A. Oneren, On a class of two dimensional (w, q)-Bernoulli and (w, q)-Euler polynomials: Properties and location of zeros, J. Com. Anal. Appl. 16 (2014), 282-292.
  10. H. Ozden, Y. Simsek, A new extension of q-Euler numbers and polynomials related to their interpolation functions., Appl. Math. Lett. 21 (2008), 934-939. https://doi.org/10.1016/j.aml.2007.10.005
  11. R. Jagannathan, K.S. Rao, Two-parameter quantum algebras, twin-basic numbers, and associasted generalized hypergeometric series, arXiv:math/0602613[math.NT].
  12. H.F. Jackson, q-Difference equations, Am. J. Math. 32 (1910), 305-314. https://doi.org/10.2307/2370183
  13. C.S. Ryoo, A Note on the Zeros of the q-Bernoulli Polynomials, J. Appl. Math. & Informatics 28 (2010), 805-811.
  14. C.S. Ryoo, Reflection Symmetries of the q-Genocchi Polynomials, J. Appl. Math. & Informatics 28 (2010), 1277-1284.
  15. C.S. Ryoo, On degenerate q-tangent polynomials of higher order, J. Appl. Math. & Informatics 35 (2017), 113-120. https://doi.org/10.14317/jami.2017.113
  16. P.N. Sadjang, On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulae, arXiv:1309.3934[math.QA].
  17. W.J. Trjitzinsky, Analytic theory of linear q-difference equations, Acta Math. 61 (1933), 1-38. https://doi.org/10.1007/BF02547785
  18. C. Xu, M. Zhang, W. Zhu, Some evaluation of q-analogues of Euler sums, Mon. Math. 182 (2017), 957-975. https://doi.org/10.1007/s00605-016-0915-z