×

zbMATH — the first resource for mathematics

Zeros of Stieltjes and Van Vleck polynomials. (English) Zbl 0417.30009

MSC:
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
33E99 Other special functions
34A05 Explicit solutions, first integrals of ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] M. Bocher, Über die Reihenentwickelungen der Potentialtheoreie, Teubner, Leipzig, 1894, pp. 215-218.
[2] E. Heine, Handbuch der Kugelfunctionen, Bd. I , G. Reimer, Berlin, 1878, pp. 472-476.
[3] F. Klein, Über lineare Differentialgleichungen der zweiten Ordnung, Göttingen, 1894, pp. 211-218. · JFM 26.0334.01
[4] F. Lucas, Propriétés géométriques des fractions rationnelles, C. R. Acad. Sci. Paris 77 (1874), 431-433; ibid. 78 (1874), 140-144; ibid. 78 (1874), 180-183; ibid. 78 (1874), 271-274.
[5] Morris Marden, Geometry of polynomials, Second edition. Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. · Zbl 0162.37101
[6] Morris Marden, On Stieltjes polynomials, Trans. Amer. Math. Soc. 33 (1931), no. 4, 934 – 944. · Zbl 0003.12402
[7] G. Pólya, Sur un théorème de Stieltjes, C. R. Acad. Sci. Paris 155 (1912), 767-769. · JFM 43.0145.04
[8] T. J. Stieltjes, Sur certains polynômes, Acta Math. 6 (1885), no. 1, 321 – 326 (French). Qui vérifient une équation différentielle linéaire du second ordre et sur la theorie des fonctions de Lamé. · JFM 17.0310.01 · doi:10.1007/BF02400421 · doi.org
[9] G. SzegÖ, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1967. · JFM 65.0278.03
[10] E. B. van Vleck, On the polynomials of Stieltjes, Bull. Amer. Math. Soc. 4 (1898), no. 9, 426 – 438. · JFM 29.0283.02
[11] Neyamat Zaheer and Mahfooz Alam, On the zeros of Stieltjes and Van Vleck polynomials, Trans. Amer. Math. Soc. 229 (1977), 279 – 288. · Zbl 0315.34035
[12] Neyamat Zaheer, On Stieltjes and Van Vleck polynomials, Proc. Amer. Math. Soc. 60 (1976), 169 – 174 (1977). · Zbl 0372.30002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.