Shifted Generalized Pascal Matrices in the Context of Clifford Algebra-Valued Polynomial Sequences

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.

[1]  M. I. Falcão,et al.  Laguerre derivative and monogenic Laguerre polynomials: An operational approach , 2011, Math. Comput. Model..

[2]  Lidia Aceto,et al.  The Matrices of Pascal and Other Greats , 2001, Am. Math. Mon..

[3]  Polynomials satisfying a binomial theorem , 1970 .

[4]  D. Peña.  Shifted Appell Sequences in Clifford Analysis , 2011, 1102.4373.

[5]  Daniel J. Velleman,et al.  Pascal's Matrices , 1993 .

[6]  L. Aceto,et al.  A matrix approach to Sheffer polynomials , 2017 .

[7]  R. Lávička.  Complete Orthogonal Appell Systems for Spherical Monogenics , 2011, 1106.2970.

[8]  P. Appell,et al.  Sur une classe de polynômes , 1880 .

[9]  Helmuth R. Malonek,et al.  A hypercomplex derivative of monogenic functsions in and its Applications , 1999 .

[10]  M. I. Falcão,et al.  A Matrix Recurrence for Systems of Clifford Algebra-Valued Orthogonal Polynomials , 2014 .

[11]  V. Souček,et al.  The Gelfand-Tsetlin bases for spherical monogenics in dimension 3 , 2010, 1010.1615.

[12]  H. Malonek,et al.  Matrix approach to hypercomplex Appell polynomials , 2016, 1602.04167.

[13]  D. Trigiante,et al.  Special polynomials as continuous dynamical systems , 2010 .

[14]  H. Malonek,et al.  A unified matrix approach to the representation of Appell polynomials , 2014, 1406.1444.

[15]  M. I. Falcão,et al.  Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials , 2017 .

[16]  M. I. Falcão,et al.  Generalized Exponentials through Appell sets in Rn+1 and Bessel functions , 2007 .