873
Views
2
CrossRef citations to date
0
Altmetric
Research Article

A new class of Gould-Hopper-Eulerian-type polynomials

Pages 283-306 | Received 27 Jan 2022, Accepted 12 Mar 2022, Published online: 04 Apr 2022

References

  • Gould HW, Hopper AT. Operational formulas connected with two generalizations of Hermite polynomials. Duke Math J. 1962;29:51–63.
  • Khan S, Raza N. Determinantal approach to certain mixed special polynomials related to Gould–Hopper polynomial. Appl Math Comp. 2015;251:599–614.
  • Bayad A, Kim T. Identities for Apostol-type Frobenius–Euler polynomials resulting from the study of a nonlinear operator. Russ J Math Phys. 2016;23:164–171.
  • Masjed-Jamei M, Koepf W. Symbolic computation of some power-trigonometric series. Symb Comput. 2017;80:273–284.
  • Dere R, Simsek Y, Srivastava HM. A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra. J Number Theory. 2013;133:3245–3263.
  • He Y, Araci S, Srivastava HM. Some new formulas for the products of the Apostol type polynomials. Adv Differ Equ. 2016;2016:1–18. (Article ID 287).
  • He Y, Araci S, Srivastava HM, et al. Some new identities for the Apostol–Bernoulli polynomials and the Apostol–Genocchi polynomials. Appl Math Comput. 2015;262:31–41.
  • Kim DS, Kim T, Lee H. A note on degenerate Euler and Bernoulli polynomials of complex variable. Symmetry. 2019;11(9):1–16. DOI:10.3390/sym11091168
  • Luo Q-M. Apostol-Euler polynomials of higher order and Gaussian hypergeometric functions. Taiwanese J Math. 2006;10:917–925.
  • Luo Q-M. Extensions of the Genocchi polynomials and their Fourier expansions and integral representations. Osaka J Math. 2011;48:291–309.
  • Luo Q-M, Srivastava HM. Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials. J Math Anal Appl. 2005;308:290–302.
  • Lu D-Q, Srivastava HM. Some series identities involving the generalized Apostol type and related polynomials. Comput Math Appl. 2011;62:3591–3602.
  • Masjed-Jamei M, Beyki MR, Koepf W. A new type of Euler polynomials and numbers. Mediterr J Math. 2018;15(138):1–17.
  • Yasmin G, Muhyi A. Certain results of 2-variable q-generalized tangent-Apostol type polynomials. J Math Comput Sci. 2020;22:238–251.
  • Srivastava HM, Kızılate C. A parametric kind of the Fubini-type polynomials. RACSAM Rev R Acad Cienc Exactas Fís Nat Ser A Mat. 2019;113:3253–3267.
  • Srivastava HM, Masjed-Jamei M, Beyki MR. A parametric type of the Apostol–Bernoulli, Apostol–Euler and Apostol–Genocchi polynomials. Appl Math Inform Sci. 2018;12:907–916.
  • Kilar N, Simsek Y. Two parametric kinds of Eulerian-type polynomials associated with Euler's formula. Symmetry. 2019;11:1–19. DOI:10.3390/sym11091097
  • Cocolicchio D, Dattoli G, Srivastava HM, editors. Advanced special functions and applications. Proceedings of the First Melfi School on Advanced Topics in Mathematics and Physics. Rome: Aracne Editrice; 2000.
  • Khan S, Raza N, Ali M. Finding mixed families of special polynomials associated with Appell sequences. J Math Anal Appl. 2017;447(1):398–418.
  • Muhyi A, Araci S. A note on q-Fubini-Appell polynomials and related properties. J Funct Spaces. 2021;2021:1–9. DOI:10.1155/2021/3805809.
  • Srivastava HM, Özarslan MA, Yılmaz B. Some families of differential equations associated with the Hermite-based Appell polynomials and other classes of Hermite-based polynomials. Filomat. 2014;28(4):695–708.
  • Srivastava HM, Araci S, Khan WA, et al. A note on the truncated-exponential based Apostol-type polynomials. Symmetry. 2019;11(4):1–20. DOI:10.3390/sym11040538
  • Srivastava HM, Srivastava R, Muhyi A, et al. Construction of a new family of Fubini-type polynomials and its applications. Adv Difference Equ. 2021;2021(1):1–25.
  • Yasmin G, Muhyi A. Certain results of hybrid families of special polynomials associated with Appell sequences. Filomat. 2019;33(12):3833–3844.
  • Yasmin G, Muhyi A. Extended forms of Legendre-Gould-Hopper-Appell polynomials. Adv Stud Contemp Math. 2019;29(4):489–504.