Journal of applied mathematics & informatics

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

DOI QR Code

STUDIES ON PROPERTIES AND CHARACTERISTICS OF TWO NEW TYPES OF q-GENOCCHI POLYNOMIALS

  • Received : 2020.08.08
  • Accepted : 2020.11.01
  • Published : 2021.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we construct q-cosine and sine Genocchi polynomials using q-analogues of addition, subtraction, and q-trigonometric function. From these polynomials, we obtain some properties and identities. We investigate some symmetric properties of q-cosine and sine Genocchi polynomials. Moreover, we find relations between these polynomials and others polynomials.

Keywords

References

  1. G.E. Andrews, D. Crippa, K. Simon, q-Series arising from the study of random graphs, SIAM J. Discrete Math. 10 (1997), 41-56. https://doi.org/10.1137/S0895480194262497
  2. L. Carlitz, Degenerate Stiling, Bernoulli and Eulerian numbers, Utilitas Math. 15, (1979), 51-88.
  3. C.A. Charalambides, On the q-differences of the generalized q-factorials, J. Statist. Plann. Inference 54, (1996), 31-43. https://doi.org/10.1016/0378-3758(95)00154-9
  4. H. Exton, q-hypergeometric Functions and Applications, Halstead Press, New York, 1983.
  5. G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Online ISBN: 9780511526251, 2004.
  6. H.F. Jackson, q-Difference equations, Am. J. Math. 32 (1910), 305-314. https://doi.org/10.2307/2370183
  7. H.F. Jackson, On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 46 (2013), 253-281. https://doi.org/10.1017/S0080456800002751
  8. V. Kac, C. Pokman, Quantum Calculus Universitext, Springer, New York, 2002.
  9. J.Y. Kang, C.S. Ryoo, Various structures of the roots and explicit properties of q-cosine Bernoulli polynomials and q-sine Bernoulli polynomials, Mathematics 8 (2020), 1-18. https://doi.org/10.3390/math8010001
  10. A. Kemp, Certain q-analogues of the binomial distribution, Sankhya A 64 (2002), 293-305.
  11. T. Kim, C.S. Ryoo, Some identities for Euler and Bernoulli polynomials and their zeros, Axioms 7 (2018), 1-19. https://doi.org/10.3390/axioms7010001
  12. H. Liu, W. Wang, Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums, Discrete Math. 309 (2009), 3346-3363. https://doi.org/10.1016/j.disc.2008.09.048
  13. N.I. Mahmudov, M. Momenzadeh, On a class of q-Bernoulli, q-Euler, and q-Genocchi polynomials, Abstr. Appl. Anal. 2014 (2014), 696454.
  14. M.J. Park, J.Y. Kang, A study on the cosine tangent polynomials and sine tangent polynomials, J. Appl. Pure Math. 2 (2020), 47-56.
  15. D. Rawlings, Limit formulas for q-exponential functions, Discrete Math. 126 (1994), 379-383. https://doi.org/10.1016/0012-365X(94)90281-X
  16. C.S. Ryoo, J.Y. Kang, Explicit properties of q-cosine and q-sine Euler polynomials containing symmetric structures, Symmetry 12 (2020), 1-21. https://doi.org/10.3390/sym12010001
  17. C.S. Ryoo, Some Properties of the (h; p; q)-Euler numbers and polynomials and computation of their zeros, J. Appl. Pure Math. 1 (2019), 1-10.
  18. A.C. Sparavigna, Graphs of q-exponentials and q-trigonometric functions, Hal HAL Id: hal-01377262 (2016), 1-8.