Nodal statistics for the Van Vleck polynomials

Communications in Mathematical Physics

Volumn 230, Issue 3, 2002, Pages 503-516

  Bourget, Alain ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036026979     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-002-0718-z     Document Type: Article

References (12)

1. [B] Bourget, A.: Nodal Statistics of the Lamé Ensemble. Ph.D. Dissertation, McGill University, 2001
2. [BT] Bourget, A., Toth, J.A.: Asymptotic statistics of zeroes for the Lamé ensemble. Commun. Math. Phys. 222(3), 475-493 (2001)
3. [G] Grünbaum, F.: Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. J. Comput. App. Math. 99, 189-194 (1998)
4. [KN] Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: Wiley-Interscience Publ., 1974
5. [M] Marden, M.: Geometry of Polynomials. Second edition, Mathematical surveys No. 3, Providence, RI: AMS
6. [MS] Martinez-Finkelshtein, A., Saff, E.B.: Asymptotic properties of Van Vleck and Stieltjes polynomials. To appear in J. Approx. Theory
7. [Sh1] Shah, G.M.: On the zeros of Van Vleck polynomials. Proc. Am. Math. Soc. 19, 1421-1426 (1970)
8. [Sh2] Shah, G.M.: Monotonic variation of zeros of Stieltjes and Van Vleck polynomials. J. Ind. Math. Soc. 33, 85-92 (1969)
9. [St] Stieltjes, T.J.: Sur certains polynômes qui vérifient une équation différentielle linéaire du second ordre et sur la théorie des fonctions de Lamé. Acta Math. 8, 321-326 (1885)
10. [Sz] Szegö, G.: Orthogonal Polynomials. Third edition, Vol. 23, Providence, RI: Am. Math. Soc., 1967
11. [T] Toth, J.A.: The quantum C. Neuman problem. Inter. Math. Res. Notices 5, 137-139 (1993)
12. [V] Van Vleck, E.B.: On the polynomials of Stieltjes. Bull. Am. Math. Soc. 4, 426-438 (1898)