Article

Journal of Applied Mathematics and Computing

, Volume 35, Issue 1, pp 497-505

First online:

Inversion of Catalan matrix plus one

  • Predrag StanimirovićAffiliated withDepartment of Mathematics, Faculty of Science, University of Niš Email author 
  • , Stefan StanimirovićAffiliated withDepartment of Mathematics, Faculty of Science, University of Niš

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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 number Catalan matrix Pascal matrix Generalized hypergeometric function Matrix inverse Resolvent

Mathematics Subject Classification (2000)

15A09 05A10 05A19