A Study of the Second-Kind Multivariate Pseudo-Chebyshev Functions of Fractional Degree
Date
2020
Authors
Ricci, Paolo Emilio
Srivastava, Rekha
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
Abstract
Here, in this paper, the second-kind multivariate pseudo-Chebyshev functions of fractional degree are introduced by using the Dunford–Taylor integral. As an application, the problem of finding matrix roots for a wide class of non-singular complex matrices has been considered. The principal value of the fixed matrix root is determined. In general, by changing the determinations of the numerical roots involved, we could find nr roots for the n-th root of an r×r matrix. The exceptional cases for which there are infinitely many roots, or no roots at all, are obviously excluded.
Description
Keywords
hypergeometric functions, classical orthogonal polynomials, second-kind pseudo-Chebyshev functions, recurrence relations, Dunford-Taylor integral, matrix powers, matrix roots
Citation
Ricci, P. E. & Srivastava, R. (2020). A study of the second-kind multivariate pseudo-Chebyshev functions of fractional degree. Mathematics, 8(6). https://doi.org/10.3390/math8060978