Hankel determinants of some polynomials arising in combinatorial analysis

Numerical Algorithms

Volumn 24, Issue 1-2, 2000, Pages 179-193

  Wimp, Jet ^a  

^a DREXEL UNIVERSITY   (United States)

Author keywords

Bessel polynomials; Combinatorial analysis; Gegenbauer polynomials; Hankel determinants; Moment problems; Orthogonal polynomials; Pollaczek polynomials

Indexed keywords

EID: 0034416249     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019197311168     Document Type: Article

References (11)

1. G.E. Andrews, R. Askey and R. Roy, Special Functions (Cambridge Univ. Press, Cambridge, 1999).
2. R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985).
3. J.L. Burchnall, Some determinants with hypergeometric elements, Proc. Edinburgh Math. Soc. (1.2) 9 (1952) 151-157.
4. A. Erdélyi et al., Higher Transcendental Functions, Vols. 1-3 (McGraw-Hill, New York, 1953).
5. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980).
6. R.L. Graham, M. Grötschel and L. Lovász, Handbook of Combinatorics, Vols. 1-2 (Elsevier Science, The Netherlands, 1995).
7. E. Grosswald, Bessel Polynomials (Springer, New York, 1978).
8. M. Petkovsek, H.S. Wilf and D. Zeilberger, A = B (A.K. Peters, Wellesley, MA, 1996).
9. C. Radoux, Calcul effectif de certains déterminants de Hankel, Bull. Soc. Math. Belg. Sér. B 31 (1979) 49-55.
10. C. Radoux, Addition formulas for polynomials built on classical combinatorial sequences, in: Proc. of ICAM Conf., Leuven, Belgium (July 1998).
11. R. Vein and P. Dale, Determinants and Their Applications in Mathematical Physics (Springer, New York, 1999).