Journal of Applied Mathematics and Computing

, Volume 35, Issue 1, pp 497–505

Inversion of Catalan matrix plus one

Authors

    • Department of Mathematics, Faculty of ScienceUniversity of Niš
  • Stefan Stanimirović
    • Department of Mathematics, Faculty of ScienceUniversity of Niš
Article

DOI: 10.1007/s12190-009-0373-z

Cite this article as:
Stanimirović, P. & Stanimirović, S. J. Appl. Math. Comput. (2011) 35: 497. doi:10.1007/s12190-009-0373-z
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Abstract

Motivated by a statistical problem, in (Aggarwala and Lamoureux in Am. Math. Mon., 109:371–377, 2002) it is shown how to invert a linear combination of the Pascal matrix with the identity matrix. Continuing this idea, we invert various linear combinations of the Catalan matrix, introduced in (Stanimirović et al. in Appl. Math. Comput. 215:796–805, 2009), with the identity matrix. In (Aggarwala and Lamoureux in Am. Math. Mon., 109:371–377, 2002) the occurrence of the polylogarithm function is observed. Inverses of linear combinations of the Catalan and the identity matrix are expressed in terms of Catalan numbers, the pochhammer function and the generalized hypergeometric function.

Catalan numberCatalan matrixPascal matrixGeneralized hypergeometric functionMatrix inverseResolvent

Mathematics Subject Classification (2000)

15A0905A1005A19

Copyright information

© Korean Society for Computational and Applied Mathematics 2010