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E. K. Leinartas and O. A. Shishkina, The discrete analog of the Newton-Leibniz formula in the problem of summation over simplex lattice points, J. Sib. Fed. Univ. Math. Phys., vol. 12, pp. 503–508, 2019.Search in Google Scholar
T. Cuchta and R. Luketic, Discrete hypergeometric Legendre polynomials, Mathematics, vol. 9, no. 20, p. 2546, 2021.Search in Google Scholar
L. Castilla, C. Cesarano, D. Bedoya, W. Ramírez, P. Agarwal, and S. Jain, A generalization of the Apostol-type Frobenius-Genocchi polynomials of level ι, in Fractional Differential Equations (P. Agarwal, C. Cattani, and S. Momani, eds.), Advanced Studies in Complex Systems, ch. 2, pp. 11–26, Academic Press, 2024.Search in Google Scholar
H. Hassani, Z. Avazzadeh, P. Agarwal, M. J. Ebadi, and A. Bayati Eshkaftaki, Generalized Bernoulli-Laguerre polynomials: Applications in coupled nonlinear system of variable-order fractional PDEs, J. Optim. Theory Appl, vol. 200, no. 1, pp. 371–393, 2024.Search in Google Scholar
A. A. Attiya, A. M. Lashin, E. E. Ali, and P. Agarwal, Coefficient bounds for certain classes of analytic functions associated with Faber polynomial, Symmetry, vol. 13, no. 2, p. 302, 2021.Search in Google Scholar
S. Albosaily, Y. Quintana, A. Iqbal, and W. Khan, Lagrange-based hypergeometric Bernoulli polynomials, Symmetry, vol. 14, no. 125, 2022.Search in Google Scholar
Y. Quintana, Generalized mixed type Bernoulli-Gegenbauer polynomial, Kragujevac J. Math, vol. 47, no. 2, pp. 245–257, 2023.Search in Google Scholar
Y. Quintana, W. Ramírez, and A. Urieles, On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, vol. 55, no. 3, pp. 1–29, 2018.Search in Google Scholar
Y. Quintana and H. Torres-Guzmán, Some relations between the Riemann zeta function and the generalized Bernoulli polynomials of level m, Univers. J. Math. Appl, vol. 2, no. 4, pp. 188–201, 2019.Search in Google Scholar
Y. Quintana and A. Urieles, Quadrature formulae of Euler-Maclaurin type based on generalized Euler polynomials of level m, Bull. Comput. Appl. Math, vol. 6, no. 2, pp. 43–64, 2018.Search in Google Scholar
D. Peralta, Y. Quintana, and S. A. Wani, Mixed-type hypergeometric Bernoulli-Gegenbauer polynomials, Mathematics, vol. 11, no. 18, p. 3920, 2023.Search in Google Scholar
L. Comtet, Advanced Combinatorics: The art of Finite and Infinite Expansions, 2nd ed.; D. Reidel Publishing Company, Inc.: Boston, USA, 1974.Search in Google Scholar
L. Kargin and V. Kurt, On the generalization of the Euler polynomials with the real parameters, Appl. Math. Comput, vol. 218, no. 3, pp. 856–859, 2011.Search in Google Scholar
F. T. Howard, Some sequences of rational numbers related to the exponential function, Duke Math. J, vol. 34, pp. 701–716, 1967.Search in Google Scholar
A. Hassen and H. D. Nguyen, Hypergeometric Bernoulli polynomials and Appell sequences, Int. J. Number Theory, vol. 4, no. 5, pp. 767–774, 2008.Search in Google Scholar
R. Booth and A. Hassen, Hypergeometric Bernoulli polynomials, J. Algebra Number Theory, vol. 2, no. 1, pp. 1–7, 2011.Search in Google Scholar
S. Hu and M.-S. Kim, On hypergeometric Bernoulli numbers and polynomials, Acta Math. Hungar, vol. 154, pp. 134–146, 2018.Search in Google Scholar
P. E. Ricci and P. Natalini, Hypergeometric Bernoulli polynomials and r-associated Stirling numbers of the second kind, Integers, vol. 22, no. #A56, 2022.Search in Google Scholar
P. Natalini and A. Bernardini, A generalization of the Bernoulli polynomials, J. Appl. Math, vol. 2003, no. 3, pp. 155–163, 2003.Search in Google Scholar
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, 1st ed.; Ellis Horwood Ltd.: West Sussex, England, 1984.Search in Google Scholar
H. M. Srivastava and J. Choi, Zeta and q-zeta Functions and Associated series and Integrals, 1st ed.; Elsevier: London, UK, 2012.Search in Google Scholar
P. Hernández-Llanos, Y. Quintana, and A. Urieles, About extensions of generalized Apostol-type polynomials, Results Math, vol. 68, pp. 203–225, 2015.Search in Google Scholar
G. Szegø, Orthogonal Polynomials, 4th ed.; Amer. Math. Soc.: Providence, Rhode Island, USA, 1975.Search in Google Scholar
R. Askey, Orthogonal Polynomials and Special Functions, 1st ed.; Reg. Conf. Series in Appl. Math. 21 SIAM: Philadelphia, USA, 1975.Search in Google Scholar
L. C. Andrews, Special Functions for Engineers and Applied Mathematicians, 1st ed Macmillan Publishing Company New York USA, 1985.Search in Google Scholar
N. M. Temme, Special Functions. An Introduction to the classical Functions of Mathematical Physics, 1st ed.; John Wiley & Sons Inc.: New York, USA, 1996.Search in Google Scholar
V. G. Paschoa, D. Pérez, and Y. Quintana, On a theorem by Bojanov and Naidenov applied to families of Gegenbauer-Sobolev polynomials, Commun. Math. Anal, vol. 16, pp. 9–18, 2014.Search in Google Scholar
H. Pijeira, Y. Quintana, and W. Urbina, Zero location and asymptotic behavior of orthogonal polynomials of Jacobi-Sobolev, Rev. Col. Mat, vol. 35, pp. 77–97, 2001.Search in Google Scholar
C. Cesarano, Generalized Chebyshev polynomials, Hacet. J. Math. Stat, vol. 3, no. 5, pp. 731–740, 2014.Search in Google Scholar
C. Cesarano and D. Assante, A note on generalized Bessel functions, Int. J. Math. Models Methods Appl. Sci, vol. 7, no. 6, pp. 625–629, 2014.Search in Google Scholar
C. Cesarano, G. M. Cennamo, and L. Placidi, Humbert polynomials and functions in terms of Hermite polynomials towards applications to wave propagation, WSEAS Trans. Math, vol. 13, pp. 595–602, 2014.Search in Google Scholar
C. Cesarano, B. Germano, and P. E. Ricci, Laguerre-type Bessel functions, Integral Transforms Spec. Funct, vol. 16, no. 4, pp. 315–322, 2005.Search in Google Scholar
