10.1007/s40096-022-00466-0

Differential and integrodifferential equations for Gould–Hopper–Frobenius–Euler polynomials

Show Details XML
  • Shabir Ahmad Mir1,
  • K. S. Nisar2,
  • Tawheeda Akhter3,
  • Serkan Araci*4,
  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, IN
  2. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, 11991, SA
  3. Department of Mathematics, University of Kashmir, Srinagar, 190006, IN
  4. Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep, 27410, TR

Published in Issue 2022-03-30

How to Cite

Mir, S. A., Nisar, K. S., Akhter, T., & Araci, S. (2022). Differential and integrodifferential equations for Gould–Hopper–Frobenius–Euler polynomials. Mathematical Sciences, 17(3 (September 2023). https://doi.org/10.1007/s40096-022-00466-0
Crossref
Scopus
Google Scholar
Europe PMC

Abstract

Abstract The fundamental aim of this paper is to derive the recurrence relation, shift operators, differential, integrodifferential and partial differential equations for Gould–Hopper–Frobenius–Euler polynomials using factorization method, which may be utilised in solving some emerging problems in different branches of science and technology.

Keywords

  • Recurrence relation,
  • Shift operators,
  • Differential equation,
  • Integro-differential equation,
  • Partial differential equation

References

  1. Infeld and Hull (1951) The factorization method (pp. 21-68) https://doi.org/10.1103/RevModPhys.23.21
  2. Frobenius, F.G.: Uber die Bernoullischen Zahlen und die Eulerischen polynome. Sitzungsber. K. Preubischen Akad. Wissenschaft. Berlin, pp. 809–847 (1910)
  3. Carlitz (1959) Eulerian numbers and polynomials (pp. 247-260) https://doi.org/10.2307/3029225
  4. Gould and Hopper (1962) Operational formulas connected with two generalizations of Hermite polynomials (pp. 15-63) https://doi.org/10.1215/S0012-7094-62-02907-1
  5. Wani and Khan (2019) Properties and applications of the Gould–Hopper–Frobenius–Euler polynomials 12(1) (pp. 93-104)
  6. He and Ricci (2002) Differential equation of Appell polynomials via the factorization method (pp. 231-237) https://doi.org/10.1016/S0377-0427(01)00423-X
  7. Özarslan and Yilmaz (2014) A set of finite order differential equations for the Appell polynomials (pp. 108-116) https://doi.org/10.1016/j.cam.2013.08.006
  8. Wani et al. (2020) Differential and integral equations for the Laguerre–Gould–Hopper based Appell and related polynomials (pp. 617-646) https://doi.org/10.1007/s40590-019-00239-1
  9. Riyasat et al. (2018) On some classes of differential equations and associated integral equations for the Laguerre–Appell polynomials 9(3) (pp. 185-194) https://doi.org/10.1515/apam-2017-0079
  10. Khan et al. (2018) Differential and integral equations associated with some hybrid families of Legendre polynomials 11(1) (pp. 127-139)
  11. Khan, S., Wani, S.A.: A note on Differential and integral equations for the Laguerre–Hermite polynomials. In: Proceedings of the Second International Conference on Computer and Communication Technologies, IC3T 2017, Advances in Intelligent Systems and Computing, vol.
  12. 381
  13. , pp. 547–555 (2016)
  14. Khan and Wani (2018) A note on differential and integral equations for the Legendre–Hermite polynomials 7(4) (pp. 514-520)
  15. Araci et al. (2017) Differential and integral equations for the 3-variable Hermite–Frobenius–Euler and Frobenius–Genocchi polynomials 11(5) (pp. 1-11)
  16. Dattoli et al. (1997) A note on the monomiality principle and generalized polynomials (pp. 98-111) https://doi.org/10.1006/jmaa.1998.6080
  17. Sandor and Crstici (2004) Kluwer Academic Publishers https://doi.org/10.1007/1-4020-2547-5
  18. Srivastava et al. (2014) Some families of differential equations associated with the Hermite-based Appell polynomials and other classes of Hermite-based polynomials 28(4) (pp. 695-708) https://doi.org/10.2298/FIL1404695S
  19. Yilmaz and Özarslan (2013) Differential equations for the extended 2D Bernoulli and Euler polynomials (pp. 1-16)
  20. Yilmaz and Özarslan (2015) Frobenius–Euler and Frobenius–Genocchi polynomials and their differential equations 3(2) (pp. 17-21)