Abstract
The paper shows the role of shifted generalized Pascal matrices in a matrix representation of hypercomplex orthogonal Appell systems. It extends results obtained in previous works in the context of Appell sequences whose first term is a real constant to sequences whose initial term is a suitable chosen polynomial of n variables.
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References
Aceto, L., Cação, I.: A matrix approach to Sheffer polynomials. J. Math. Anal. Appl. 446, 87–100 (2017)
Aceto, L., Malonek, H.R., Tomaz, G.: A unified matrix approach to the representation of Appell polynomials. Integral Transforms Spec. Funct. 26, 426–441 (2015)
Aceto, L., Malonek, H.R., Tomaz, G.: Matrix approach to hypercomplex Appell polynomials. Appl. Num. Math. 116, 2–9 (2017)
Aceto, L., Trigiante, D.: The matrices of Pascal and other greats. Amer. Math. Monthly 108, 232–245 (2001)
Aceto, L., Trigiante, D.: Special polynomials as continuous dynamical systems. In: Cialdea, A., Dattoli, G., He, M.X., Shrivastava, H.M. (eds.) Lecture Notes of Seminario Interdisciplinare di Matematica, vol. 9, pp. 33–40 (2010)
Appell, P.: Sur une classe de polynômes. Ann. Sci. École Norm. Sup. 9(2), 119–144 (1880)
Bock, S., Gürlebeck, K., Lávička, R., Souček, V.: Gelfand-Tsetlin bases for spherical monogenics in dimension 3. Rev. Mat. Iberoam. 28(4), 1165–1192 (2012)
Cação, I., Falcão, M.I., Malonek, H.R.: Laguerre derivative and monogenic Laguerre polynomials: an operational approach. Math. Comput. Modelling 53, 1084–1094 (2011)
Cação, I., Falcão, M.I., Malonek, H.R.: A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials. Adv. Appl. Clifford Algebras 24, 981–994 (2014)
Cação, I., Falcão, M.I., Malonek, H.R.: Three-term recurrence relations for systems of Clifford algebra-valued orthogonal polynomials. Adv. Appl. Clifford Algebras 27, 71–85 (2017)
Call, G.S., Velleman, D.J.: Pascal’s matrices. Am. Math. Monthly 100(4), 372–376 (1993)
Carlson, B.C.: Polynomials satisfying a binomial theorem. J. Math. Anal. Appl. 32, 543–558 (1970)
Falcão, M.I., Malonek, H.R.: Generalized exponentials through Appell sets in \(\mathbb{R}^{n+1}\) and Bessel functions. In: Simos, T.E., Psihoyios, G., Tsitouras, C. (eds.) AIP Conference Proceedings, vol. 936, pp. 738–741 (2007)
Gürlebeck, K., Malonek, H.R.: A hypercomplex derivative of monogenic functions in \(\mathbb{R}^{m+1}\) and its applications. Complex Variables 39, 199–228 (1999)
Lávička, R.: Complete orthogonal Appell systems for spherical monogenics. Complex Anal. Oper. Theory 6, 477–489 (2012)
Peña Peña, D.: Shifted Appell sequences in Clifford analysis. Results Math. 63, 1145–1157 (2013)
Acknowledgments
This work was supported in part by the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), through CIDMA-Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.
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Cação, I., Malonek, H.R., Tomaz, G. (2017). Shifted Generalized Pascal Matrices in the Context of Clifford Algebra-Valued Polynomial Sequences. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10405. Springer, Cham. https://doi.org/10.1007/978-3-319-62395-5_28
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DOI: https://doi.org/10.1007/978-3-319-62395-5_28
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