Journal of applied mathematics & informatics

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

DOI QR Code

A STUDY ON q-SPECIAL NUMBERS AND POLYNOMIALS WITH q-EXPONENTIAL DISTRIBUTION

  • Received : 2018.01.16
  • Accepted : 2018.06.18
  • Published : 2018.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce q-special numbers and polynomials with q-exponential distribution. From these numbers and polynomials we derive some properties and identites. We also find approximated zeros of q-special polynomials and investigate property of two parameters ${\lambda}$, q.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. W.M. Albert, O. Ingram, A multivatiate exponential distribution, Boeing scientific research laboratories 450 March (1966).
  2. M. Ahsanullah, Linear prediction of record values for the two parameter exponential distribution, Ann. Inst. Stat. Math. 32 (1980), 363368. https://doi.org/10.1007/BF02480340
  3. B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, Records, New York: John Wiley.
  4. B. Epstein, The exponential distribution and its role in life testing, Industrial Quality Control 15 (1958), 2-7.
  5. T.S. Ferguson, A characterization of the exponential distribution, Ann. Math. Statist 35 (1964), 1199-1207. https://doi.org/10.1214/aoms/1177703277
  6. J.E. Freund, A bivariate extension of the exponential distribution, J. Amer. Statist. Assoc. 56 (1961), 971-977. https://doi.org/10.1080/01621459.1961.10482138
  7. E.J. Gumbel, Bivariate exponential distributions, J. Amer. Statist. Assoc. 55 (1960), 698-707. https://doi.org/10.1080/01621459.1960.10483368
  8. N. Glick, Breaking record and breaking boards, Amer. Math. 85 (1978), 226.
  9. Ira Gessel, Richard P. Stanley, Stirling polynomials, Journal of Combinatorial Theory, Series A 24 (1978), 24-33.
  10. J.Y. Kang, Some properties of q-Euler polynomials using q-derivative and q-integral, Far East Journal of Mathematical Sciences 102 (11) (2017) 2687-2699. https://doi.org/10.17654/MS102112687
  11. J.Y. Kang, C.S. Ryoo, A research on the new polynomials involved with the central factorial numbers, Stirling numbers and others polynomials, Journal of Inequalities and Applications 2014, 2014:26 doi:10.1186/1029-242X-2014-26.
  12. Lee-Chae Jang, A study on the distribution of twisted-Genocchi polynomials, Advanced Studies in Contemporary Mathematics 18 (2) (2009), 181189.
  13. V. Nevzorov, Records: mathematical theory, Translation of Mathematical Monographs. Amer. Math. Soc., (2001) 194: Providence, RI.
  14. 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
  15. C.S. Ryoo, Differential equations associated with twisted (h, q)-tangent polynomials, J. Appl. Math. & Informatics 36 (2018), 205-212.

Cited by

  1. SOME PROPERTIES OF DEGENERATE CARLITZ-TYPE TWISTED q-EULER NUMBERS AND POLYNOMIALS vol.39, pp.1, 2018, https://doi.org/10.14317/jami.2021.001