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

Author

Listed:
  • Paolo Emilio Ricci

    (Dipartimento di Matematica, International Telematic University UniNettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada)

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.

Suggested Citation

  • Paolo Emilio Ricci & Rekha Srivastava, 2020. "A Study of the Second-Kind Multivariate Pseudo-Chebyshev Functions of Fractional Degree," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:978-:d:371969
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    References listed on IDEAS

    as
    1. Srivastava, H.M. & Riyasat, Mumtaz & Khan, Subuhi & Araci, Serkan & Acikgoz, Mehmet, 2020. "A new approach to Legendre-truncated-exponential-based Sheffer sequences via Riordan arrays⋆," Applied Mathematics and Computation, Elsevier, vol. 369(C).
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