Abstract
In this paper we investigate Hankel determinants of the form \(\left| {c_{i + j} (t)} \right|_{ij = 0,...,n} \), where c n (t) is one of a number of polynomials of combinatorial interest. We show how some results due to Radoux may be generalized, and also show how “stepped up” Hankel determinants of the form \(\left| {c_{i + j + k} (t)} \right|_{ij = 0,...,n} ,\;\;k = 1,2,...,\) may be evaluated.
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References
G.E. Andrews, R. Askey and R. Roy, Special Functions (Cambridge Univ. Press, Cambridge, 1999).
R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985).
J.L. Burchnall, Some determinants with hypergeometric elements, Proc. Edinburgh Math. Soc. (1.2) 9 (1952) 151–157.
A. Erdélyi et al., Higher Transcendental Functions, Vols. 1–3 (McGraw-Hill, New York, 1953).
I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980).
R.L. Graham, M. Grötschel and L. Lovász, Handbook of Combinatorics, Vols. 1–2 (Elsevier Science, The Netherlands, 1995).
E. Grosswald, Bessel Polynomials (Springer, New York, 1978).
M. Petkovsek, H.S. Wilf and D. Zeilberger, A = B (A.K. Peters, Wellesley, MA, 1996).
C. Radoux, Calcul effectif de certains déterminants de Hankel, Bull. Soc. Math. Belg. Sér. B 31 (1979) 49–55.
C. Radoux, Addition formulas for polynomials built on classical combinatorial sequences, in: Proc. of ICAM Conf., Leuven, Belgium (July 1998).
R. Vein and P. Dale, Determinants and Their Applications in Mathematical Physics (Springer, New York, 1999).
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Wimp, J. Hankel determinants of some polynomials arising in combinatorial analysis. Numerical Algorithms 24, 179–193 (2000). https://doi.org/10.1023/A:1019197311168
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DOI: https://doi.org/10.1023/A:1019197311168