Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barry, P.: A Catalan transform and related transformations on integer sequences. J. Integer Seq. 8, Article 05.4.5 (2005)
Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, New York (1978)
Cvetković, A., Rajković, P., Ivković, M.: Catalan numbers, the Hankel transform and Fibonacci numbers. J. Integer Seq. 5, Article 02.1.3 (2002)
Gautschi, W.: Orthogonal Polynomials: Computation and Approximation. Clarendon, Oxford (2004)
Krattenthaler, C.: Advanced determinant calculus: A complement. Linear Algebra Appl. 411 (2005) 68–166
Layman, J.W.: The Hankel transform and some of its properties. J. Integer Seq. 4, Article 01.1.5 (2001)
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)
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)
Sloane, NJA: The On-Line Encyclopedia of Integer Sequences. Published electronically at http://www.research.att.com/~njas/sequences/, 2007
Acknowledgements
This research was supported by the Science Foundation of Republic Serbia, Project No. 144023 and Project No. 144011.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
Dedicated to Professor Gradimir V. Milovanovićon the occasion of his 60th birthday
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Barry, P., Rajković, P.M., Petković, M.D. (2010). An Application of Sobolev Orthogonal Polynomials to the Computation of a Special Hankel Determinant. In: Gautschi, W., Mastroianni, G., Rassias, T. (eds) Approximation and Computation. Springer Optimization and Its Applications, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6594-3_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-6594-3_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-6593-6
Online ISBN: 978-1-4419-6594-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)