Journal of applied mathematics & informatics

  • 제41권3호
  • /
  • Pages.687-696
  • /
  • 2023
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

DIFFERENTIAL EQUATIONS CONTAINING 2-VARIABLE MIXED-TYPE HERMITE POLYNOMIALS

  • J.Y. KANG (Department of Mathematics Education, Silla University)
  • 투고 : 2023.03.06
  • 심사 : 2023.05.04
  • 발행 : 2023.05.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we introduce the 2-variable mixed-type Hermite polynomials and organize some new symmetric identities for these polynomials. We find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials.

키워드

참고문헌

  1. L.C. Andrews, Special Functions for Engineers and Mathematicians, Macmillan. Co., New York, USA, 1985.
  2. P. Appell, J. Hermitt Kampe de Feriet, Fonctions Hypergeometriques et Hyperspheriques: Polynomes d Hermite, Gauthier-Villars, Paris, France, 1926.
  3. A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, Krieger, New York, USA, 1981.
  4. G.E. Andrews, R. Askey, and R. Roy, Special Functions, Cambridge University Press, Cambridge, UK, 1999.
  5. G. Arfken, Mathematical Methods for Physicists, 3rd ed., Academic Press, Orlando, FL, USA, 1985.
  6. G. Dattoli, Generalized polynomials operational identities and their applications, J. Comput. Appl. Math. 118 (2000), 111-123. https://doi.org/10.1016/S0377-0427(00)00283-1
  7. Zhiliang Deng, Xiaomei Yang, Convergence of spectral likelihood approximation based on q-Hermite polynomials for Bayesian inverse problems, Proc. Amer. Math. Soc. 150 (2022), 4699-4713. https://doi.org/10.1090/proc/14517
  8. L. Carlitz, Degenerate Stiling, Bernoulli and Eulerian numbers, Utilitas Math. 15 (1979), 51-88.
  9. P.T. Young, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, J. Number Theorey 128 (2008), 738-758. https://doi.org/10.1016/j.jnt.2007.02.007
  10. M. Cenkci, F.T. Howard, Notes on degenerate numbers, Discrete Math. 307 (2007), 2395-2375.
  11. C. Cesarano, W. Ramirez, S. Khan, A new class of degenerate Apostol-type Hermite polynomials and applications, Dolomites Research Notes on Approximation 15 (2022), 1-10.
  12. C.S. Ryoo, R.P. Agarwal, J.Y. Kang, Some properties involving 2-variable modified partially degenerate Hermite polynomials derived from differential equations and distribution of their zeros, Dynamic Systems and Applications 29 (2020), 248-269. https://doi.org/10.46719/dsa20202924
  13. K.W. Hwang, C.S. Ryoo, Some identities involving two-variable degenerate Hermite polynomials induced from differential equations and structure of their roots, Mathematics 8 (2020). doi:10.3390/math8040632
  14. T. Kim, D.S. Kim, H.I. Kwon, C.S. Ryoo, Differential equations associated with Mahler and Sheffer-Mahler polynomials, Nonlinear Funct. Anal. Appl. 24 (2019), 453-462.
  15. C.S. Ryoo, A numerical investigation on the structure of the zeros of the degenerate Eulertangent mixed-type polynomials, J. Nonlinear Sci. Appl. 10 (2017), 4474-4484. https://doi.org/10.22436/jnsa.010.08.39
  16. C.S. Ryoo, Differential equations associated with tangent numbers, J. Appl. Math. Inform. 34 (2016), 487-494. https://doi.org/10.14317/jami.2016.487
  17. C.S. Ryoo, Some identities involving Hermitt Kampe de Feriet polynomials arising from differential equations and location of their zeros, Mathematics 7 (2019). doi:10.3390/math7010023
  18. V.I. Bogachev, Chebyshev-Hermite Polynomials and Distributions of Polynomials in Gaussian Random Variables, Theory of Probability & Its Applications 66 (2022). https://doi.org/10.1137/S0040585X97T990617