An Application of Sobolev Orthogonal Polynomials to the Computation of a Special Hankel Determinant
Many Hankel determinant computations arising in combinatorial analysis can be done using results from the theory of standard orthogonal polynomials. Here, we will emphasize special sequences which require the inclusion of discrete Sobolov orthogonality to find their closed form.
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This research was supported by the Science Foundation of Republic Serbia, Project No. 144023 and Project No. 144011.
- 1.Barry, P.: A Catalan transform and related transformations on integer sequences. J. Integer Seq. 8, Article 05.4.5 (2005)Google Scholar
- 3.Cvetković, A., Rajković, P., Ivković, M.: Catalan numbers, the Hankel transform and Fibonacci numbers. J. Integer Seq. 5, Article 02.1.3 (2002)Google Scholar
- 6.Layman, J.W.: The Hankel transform and some of its properties. J. Integer Seq. 4, Article 01.1.5 (2001)Google Scholar
- 7.Marcellán, F., Ronveaux, A.: On a class of polynomials orthogonal with respect to a discrete Sobolev inner product. Indag. Mathem. N.S. 1, 451–464 (1990)Google Scholar
- 8.Rajković, P.M., Petković, M.D., Barry, P.: The Hankel transform of the sum of consecutive generalized Catalan numbers. Integral Transform. Spec. Funct. 18 No. 4, 285–296 (2007)Google Scholar
- 9.Sloane, NJA: The On-Line Encyclopedia of Integer Sequences. Published electronically at http://www.research.att.com/~njas/sequences/, 2007