ICTAMI2007. 126KB Jun 04 2011 12:08:47 AM
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We prove that one characterization for the classical orthogonal polynomials sequences (Hermite, Laguerre, Jacobi and Bessel) cannot be extended to the semi-classical ones..
Our main results, Theorems 1 and 2 below, determine all counting GFs of these two forms and give a unified combinatorial interpretation for them in terms of colored lattice paths..
We notice that some recent explicit results about linear recurrent sequences over a ring R with 1 were already obtained by Agou in a 1971 paper by considering the euclidean division
An elementary proof is given of an arithmetic for- mula, which was stated but not proved by Liouville.. An appli- cation of this formula yields a formula for the number of
In this paper, using the maximal rank of the generalized Schur complement, a new simpler equivalent condition is obtained in terms of only the ranks of the known matrices for
In this paper, using the maximal rank of the generalized Schur complement, a new simpler equivalent condition is obtained in terms of only the ranks of the known matrices for
In this paper, we will establish the above conjecture (Theorem 2.3) and also characterize all sign patterns that require eventual nonnegativity (Theorem 2.6) in terms of
In this paper, the solutions to Dirichlet boundary value problems of nonlinear functional difference equations with Jacobi operators are investigated.. By using critical point
