Ricci, Paolo EmilioSrivastava, Rekha2020-07-162020-07-1620202020Ricci, 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/math8060978https://doi.org/10.3390/math8060978http://hdl.handle.net/1828/11937Here, 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.enhypergeometric functionsclassical orthogonal polynomialssecond-kind pseudo-Chebyshev functionsrecurrence relationsDunford-Taylor integralmatrix powersmatrix rootsArticleDepartment of Mathematics and Statistics