A Study of the Second-Kind Multivariate Pseudo-Chebyshev Functions of Fractional Degree

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 n r 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.

Keywords

• hypergeometric functions
• classical orthogonal polynomials
• second-kind pseudo-Chebyshev functions
• recurrence relations
• Dunford–Taylor integral
• matrix powers