The moment problem associated with the Stieltjes-Wigert polynomials

Journal of Mathematical Analysis and Applications

Volumn 277, Issue 1, 2003, Pages 218-245

  Christiansen, Jacob Stordal ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Indeterminate moment problem; Nevanlinna parametrization; Stieltjes Wigert polynomials

Indexed keywords

EID: 0037283138     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00534-6     Document Type: Article

References (20)

1. N.I. Akhiezer, The Classical Moment Problem, Oliver and Boyd, Edinburgh. 1965.
2. G.E. Andrews, R. Askey, Enumerations of partitions: the role of Eulerian series and q-orthogonal polynomials, in: M. Aigner (Ed.), Higher Combinatorics, D. Reidel, Dordrecht, 1977, pp. 3-260.
3. R. Askey, Limits of some q-Laguerre polynomials, J. Approx: Theory 46 (1986) 213-216.
4. R. Askey, Orthogonal polynomials and theta functions, in: L. Ehrenpreis, R.C. Gunning (Eds.), Theta Functions Bowdoin 1987, in: Proc. Symp. Pure Math., Vol. 49, Part 2, 1989, pp. 299-321.
5. R. Askey, R. Roy, More q-beta integrals, Rocky Mountain J. Math. 16 (1986) 365-372.
6. C. Berg, On some indeterminate moment problems for measures on a geometric progression, J. Comput. Appl. Math. 99 (1998) 67-75.
7. C. Berg, From discrete to absolutely continuous solutions of indeterminate moment problems, Arab. J. Math. Sci. 4 (1998) 1-18.
8. C. Berg, H.L. Pedersen, On the order and type of the entire functions associated with an indeterminate Hamburger moment problem, Ark. Mat. 32 (1994) 1-11.
9. T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
10. T.S. Chihara, A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials, Canad. Math. Bull. 13 (1970) 529-532.
11. T.S. Chihara, On generalized Stieltjes-Wigert and related orthogonal polynomials, J. Comput. Appl. Math. 5 (1979) 291-297.
12. J.S. Christiansen, The moment problem associated with the q-Laguerre polynomials, Constr. Approx, to appear.
13. G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
14. R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report no. 98-17, TU-Delft, 1998.
15. A.G. Pakes, Length biasing and laws equivalent to the log-normal, J. Math. Anal. Appl. 197 (1996) 825-854.
16. H.L. Pedersen, Stieltjes moment problems and the Friedrichs extension of a positive definite operator, J. Approx. Theory 83 (1995) 289-307.
17. H.L. Pedersen, La paramétrisation de Nevanlinna et le problème des moments de Stieltjes indéterminé, Expo. Math. 15 (1997) 273-278.
18. T.J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse 8 (1894) 1-122; Ann. Fac. Sci. Toulouse 9 (1895) 1-47; English version contained in T.J. Sfieltjes, Collected Papers, G. van Dijk (Ed.), Vol. II, Springer, Berlin, 1993.
19. L.J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894) 318-343.
20. S. Wigert, Sur les polynômes orthogonaux et l'approximation des fonctions continues, Arkiv för matematik, astronomi och fysik 17 (18) (1923).