[1] Appell P, Kampé de Fériet J. Fonctions hypergéométriques et hypersphériques. Polynomes d' Hermite. Paris:Gauthier-Villars, 1926 [2] Boas Ralph P Jr, Buck R C. Polynomial Expansions of Analytic Functions. Berlin, Göttingen, Heidelberg:Springer, 1964 [3] Bretti G, Ricci P E. Multidimensional extension of the Bernoulli and Appell polynomials. Taiwan J Math, 2004, 8(3):415-428 [4] Brickenstein M, Dreyer A. Gröbner-free normal forms for Boolean polynomials//ISSAC'08:Proceedings of the twenty-first international symposium on symbolic and algebraic computation. New York:ACM, 2008:55-62 [5] Carlitz L. A degenerate Staudt-Clausen theorem. Arch Math (Basel), 1956, 7:28-33 [6] Carlitz L. Degenerate Stirling, Bernoulli and Eulerian numbers. Utilitas Math, 1979, 15:51-88 [7] Cenkci M, Howard F T. Notes on degenerate numbers. Discrete Mathematics, 2007, 307(19/20):2359-2375 [8] Chang J H. The Gould-Hopper polynomials in the Novikov-Veselov equation. Journal of Mathematical Physics, 2011, 52(9):1-19 [9] Cheikh Y B, Zaghouani A. Some discrete d-orthogonal polynomial sets. Journal of Computational and Applied Mathematics, 2003, 156:253-263 [10] Costabile F A. Modern Umbral Calculus:An Elementary Introduction With Applications to Linear Interpolation and Operator Approximation Theory//De Gruyter-Studies In Mathematics. De Gruyter, 2019 [11] Costabile F. Expansion of real functions in Bernoulli polynomials and applications//Conf sem University Bari. IT, 1999:273 [12] Costabile F, Dell' accio F, Gualtieri M I. A new approach to Bernoulli polynomials. Rend Mat Appl, 2006, 26(7):1-12. [13] Costabile F A, Gualtieri M I, Napoli A. Recurrence relations and Determinant forms for general polynomial sequences, Application to Genocchi polynomials. Integral Transforms and Special Functions, 2019, 30(2):112-127 [14] Costabile F A, Longo E. A determinantal approach to Appell polynomials. Journal of Computational and Applied Mathematics, 2010, 234(5):1528-1542 [15] Costabile F A, Longo E. $\Delta _{h}$-Appell sequences and related interpolation problem. Numer Algor, 2013, 63:165-186 [16] Dattoli G. Generalized polynomials, operational identities and their applications. J Comput Appl Math, 2000, 118:111-123 [17] Duran U, Açıkgöz M. On generalized degenerate Gould-Hopper based fully degenerate Bell polynomials. Journal of Mathematics and Computer Science, 2020, 21:243-257 [18] Duran U, Sadjang P N. On Gould-Hopper-Based Fully Degenerate Poly-Bernoulli Polynomials with a q-Parameter. Mathematics, 2019, 7(2):1-14 [19] El-Desouky B S, Mustafa A. New Results on higher-order Daehee and Bernoulli numbers and polynomials. Adv Difference Equ, 2016, 32:1-21 [20] Gould H W, Hopper A T. Operational formulas connected with two generalization of Hermite polynomials. Duke Math J, 1962, 29(1):51-63 [21] He M X, Ricci P E. Differential equation of Appell polynomials via the factorization method. J Comput Appl Math, 2002, 139(2):231-237 [22] Jordan C. Calculus of Finite Differences. New York:Chelsea Publishing Company, 1965 [23] Khan S, Al-Gonah A A. Certain Results for the Laguerre-Gould Hopper Polynomials. Applications and Applied Mathematics, 2014, 9(2):449-466 [24] Khan W A. Degenerate Hermite-Bernoulli Numbers and Polynomials of the Second Kind. Prespacetime Journal, 2016, 7(9):1297-1305 [25] Khan W A. A Note on Degenerate Hermite Poly-Bernoulli Numbers and Polynomials. Journal of Classical Analysis, 2016, 8(1):65-76 [26] Khan S, Al-Salad M W. Summation formula for Gould-Hopper generalized Hermite polynomials. Computers and Mathematics with Applications, 2011, 61:1536-1541 [27] Khan S, Nahid T, Riyasat M. On degenerate Apostol-type polynomials and applications. Boletiın de la Sociedad Matemática Mexicana, 2019, 25:509-528 [28] Khan S, Riyaset M. Determinantal approach to certain mixed special polynomials related to Gould-Hopper polynomials. Applied Mathematics and Computation, 2015, 251:599-614 [29] Kim D S, Kim T. Poly-Cauchy and Peters mixed-type polynomials. Advances in Difference Equations, 2014, 4(1):1-18 [30] Kim D S, Kim T. Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials. Journal of Inequalities and Applications, 2014, 214(1):1-19 [31] Kim D S, Kim T, Lee S H, Seo J J. Higher-Order Daehee numbers and polynomials. Int J Math Anal, 2014, 8(5):273-283 [32] Kim T, Kim D S. Identities involving degenerate Euler numbers and polynomials arising from non linear differential equations. J Nonlinear Sci Appl, 2016, 9(5):2086-2098 [33] Kim T, Seo J J. A note on Changhee polynomials and numbers. Adv Studies Theor Phys, 2013, 7(20):993-1003 [34] Kwon H I, Kim T, Seo J J. A note on Daehee numbers arising from differential equations. Global Journal of Pure and Applied Mathematics, 2016, 12(3):2349-2354 [35] Leontév V K. Symmetric Boolean polynomials. Computational Mathematics and Mathematical Physics, 2010, 50:1447-1458 [36] Leontév V K. On Boolean polynomials. Dokl Akad Nauk, 2003, 338:593-595 [37] Lim D. Some identities of degenerate Genocchi polynomials. Bull Korean Math Soc, 2016, 53(2):569-579 [38] Lu D-Q, Luo Q-M. Some properties of the generalized Apostol-type polynomials. Boundary Value Problems, 2013, 64(1):1-13 [39] Mahmudov N I, Keleshteri M E. q-Extensions for the Apostol Type Polynomials, Journal of Applied Mathematics. Article ID 868167, 2014:1-8 [40] Özarslan M A. Unified Apostol-Bernoulli, Euler and Genocchi polynomials. Comput Math Appl, 2011, 62(6):2452-2462 [41] Özarslan M A. Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials. Adv Difference Equ, 2013, 116(1):1-13 [42] Özden H, Şimşek Y, Srivastava H M. A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials. Computers and Mathematics with Applications, 2010, 60:2779-2787 [43] Prabhakar T R, Gupta S. Bernoulli polynomials of the Second Kind and General Order. J Pure Appl Math, 1980, 11(10):1361-1368 [44] Qi F. Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind. Filomat, 2014, 28(2):319-327 [45] Qi F, Guo B-N. Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials. Mathematics, 2016, 4(4):1-11 [46] Qi F, Guo B-N. A determinantal expression and a recurrence relation for the Euler polynomials. Advances and Applications in Mathematical Sciences, 2017, 16:297-309 [47] Ricci P E. Differential Equations for Classical and Non-Classical Polynomial Sets:A Survey Axioms, 2019, 8(2):1-15 [48] Roman S. The umbral calculus. Pure and Applied Mathematics. New York:Inc (Harcourt Brace Jovanovich Publishers), 1984 [49] Srivastava H M, Kurt B, Kurt V. Identities and relations involving the modified degenerate hermite-based Apostol-Bernoulli and Apostol-Euler polynomials. Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales. Serie A. Matemáticas, 2019, 113:1299-1313 [50] Srivastava H M, Manocha H L. A Treatise on Generating Functions. John Wiley and Sons, New York, Chichester, Brisbane and Toronto:Halsted Press (Ellis Horwood Limited, Chichester), 1984 [51] Srivastava H M, Özarslan M A, Yılmaz B. Some families of differential equations associated with the Hermite based Appell polynomials. Filomat, 2014, 28(4):695-708 [52] Srivastava H M, Özarslan M A, Yaşar B Y. Difference equations for a class of twice iterated $\Delta _{h}$-Appell sequences of polynomials. Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales. Serie A. Matemáticas, 2019, 113:1851-1871 [53] Şimşek Y, So J S. On Generating Functions for Boole Type Polynomials and Numbers of Higher Order and Their Applications. Symmetry, 2019, 11(3):1-13 [54] Varma S, Yaşar B Y, Özarslan M A. Hahn-Appell polynomials and theird-orthogonality. Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales. Serie A. Matemáticas, 2019, 113:2127-2143 [55] Wang H, Liu G. An explicit formula for higher order Bernoulli polynomials of the second kind. Integer, 2013, 13:1-7 [56] Wani S A, Khan S. Properties and applications of the Gould-Hopper-Frobenius-Euler polynomials. Tbilisi Mathematical Journal, 2019, 12(1):93-104 [57] Yılmaz B, Özarslan M A. Differential Equations of the Extended 2D Bernoulli and Euler Polynomials. Advances in Difference Equations, 2013, 107(1):1-16 [58] Yılmaz Yaşar B, Özarslan M A. Frobenius-Euler and Frobenius-Genocchi polynomials and their differential equations. New Trends in Mathematical Sciences, 2015, 3:172-180 |