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Clifford–Hermite Polynomials in Fractional Clifford Analysis

  • Paula CerejeirasEmail author
  • Nelson Vieira
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 252)

Abstract

In this paper we generalize and standardize Clifford–Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann–Liouville derivative in a symbolic way. As the main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven

Keywords

Clifford analysis Hermite polynomials fractional calculus Riemann–Liouville fractional derivatives fractional Dirac operator 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.CIDMA – Center for Research and Development in Mathematics and Applications Department of MathematicsUniversity of AveiroAveiroPortugal

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