499
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Construction of partially degenerate Laguerre–Bernoulli polynomials of the first kind

, &
Pages 362-375 | Received 07 Mar 2022, Accepted 10 May 2022, Published online: 27 May 2022

References

  • Kim T. q-Volkenborn integration. Russ J Math Phys. 2002;9(3):288–299.
  • Kim T. An invariant p-adic q-L-functions. Kyushu J Math. 1994;48(1):73–86.
  • Dolgy DV, Khan WA. A note on type two degenerate poly-Changhee polynomials of the second kind. Symmetry. 2021;13(579):1–12.
  • Haroon H, Khan WA. Degenerate Bernoulli numbers and polynomials associated with hermite polynomials. Commun Korean Math Soc. 2018;33(2):651–669.
  • Dattoli G, Torre A. Operational methods and two variable Laguerre polynomials. Atti Accad Sci Torino Cl Sci Fis Mat Natur. 1998;132:3–9.
  • Andrews LC. Special functions for engineers and mathematicians. New York: Macmillan. Co.; 1985.
  • Agarwal P, Qi F, Chand M, et al. Certain integrals involving the generalized hypergeometric functions and the Laguerre polynomials. J Comput Appl Math. 2017;313(15):307–317.
  • Kwon JK, Rim SH, Park JW. A note on the Appell type Daehee polynomials. Global J Pure Appl Math. 2015;11(5):2745–2753.
  • Khan WA, Muhiuddin G, Muhyi A, et al. Analytical properties of type 2 degenerate poly-Bernoulli polynomials associated with their applications. Adv Differ Equ. 2021;2021(420):1–18.
  • Khan WA, Muhyi A, Ali R, et al. A new family of degenerate poly-Bernoulli polynomials of the second kind with its certain related properties. AIMS Math. 2021;6(11):12680–12697.
  • Qi F, Dolgy DV, Kim T. On the partially degenerate Bernoulli polynomials of the first kind. Global J Pure Appl Math. 2015;11(4):2407–2412.
  • Bohner M, Cuchta T. The generalized hypergeometric difference equation. Demonstr Math. 2018;51:62–75.
  • Border AZ. The r-Stirling numbers. Discr Math. 1984;49(3):241–259.
  • Khan WA, Araci S, Acikgoz M, et al. A new class of partially degenerate hermite-Genocchi polynomials. J Nonlinear Sci Appl. 2017;10(9):5072–5081.
  • Khan WA, Pathan MA. On generalized Lagrange-Hermite-Bernoulli and related polynomials. Acta Et Comment Univ Tartu Math. 2019;23(2):211–224.
  • Khan WA, Haroon H. Some symmetric identities for the generalized Bernoulli, euler and Genocchi polynomials associated with hermite polynomials. Springer Plus. 2016;5:1–21.
  • Khan WA, Acikgoz M, Duran U. Note on the type 2 degenerate multi-poly-Euler polynomials. Symmetry. 2020;12:1–10.
  • Khan WA, Ali R, Alzobydi KAH, et al. A new family of degenerate poly-Genocchi polynomials with its certain properties. J Funct Spaces. 2021;2021:Article ID 6660517, 8 pages.
  • Muhiuddin G, Khan WA, Duran U. Al-Kadi D: some identities of the multi poly-Bernoulli polynomials of complex variable. J Funct Spaces. 2021;2021:Article ID 7172054, 8 pages.
  • Muhiuddin G, Khan WA, Duran U. Two variable type 2 fubini polynomials. Mathematics. 2021;9(281):1–13.
  • Muhiuddin G, Khan WA, Muhyi A, et al. Some results on type 2 degenerate poly-Fubini polynomials and numbers. Comput Model Eng Sci. 2021;29(2):1051–1073.
  • Muhiuddin G, Khan WA, Al-Kadi D. Construction on the degenerate poly-Frobenius–Euler polynomials of complex variable. J Funct Space. 2021;2021:Article ID 3115424, 9 pages.
  • Irmak H, Agrawal P, Agarwal RP. The complex error functions and various extensive results together with implications pertaining to certain special functions. Turk J Math. 2022;46:662–674.
  • Pathan MA, Khan WA. Some implicit summation formulas and symmetric identities for the generalized hermite-Bernoulli polynomials. Mediterr J Math. 2015;12:679–695.