Skip to main content
Log in

On certain determinants whose elements are orthogonal polynomials

  • Published:
Journal d’Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. W. N. Bailey, On two manuscripts by Bishop Barnes,Quarterly Journal of Mathematics, Vol. 10, 1959, pp. 236–240.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bateman Manuscript Project (Director: A. Erdélyi),Higher transcendental functions, Vols 1, and 2, New York-Toronto-London 1953.

  3. E. F. Beckenbach, W. Seidel and O. Szász, Recurrent determinants of Legendre and of ultraspherical polynomials,Duke Mathematical Journal, Vol. 18, 1951, pp. 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. E. Forsythe, Second order determinants of Legendre polynomials,Duke Mathematical Journal, Vol. 18, 1951, pp. 361–371.

    Article  MATH  MathSciNet  Google Scholar 

  5. F. R. Gantmacher, Matrix Theory (Translation from the Russian),Chelsea Publishing Company, Vol. 1, 1959.

  6. W. Hahn, Ueber orthogonale polynome, dieq-Differenzengleichungen genügen,Mathematische Nachrichten, Vol. 2, 1949, pp. 4–34.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Karlin and J. L. McGregor, The differential equations of birth-and death processes, and the Stieltjes moment problem,Transactions of the American Mathematical Society, Vol. 85, 1957, pp. 489–546.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Karlin and J. L. McGregor, Coincidence properties of birth and death processes,Pacific Journal of Mathematics, Vol. 9, 1959, pp. 1109–1140.

    MATH  MathSciNet  Google Scholar 

  9. E. Mohr, Einfacher Beweis des verallgemeinerten Determinantensatzes von Sylvester nebst einer Verschärfung,Mathematische Nachrichten, Vol. 10, 1953, pp. 257–260,

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Pólya and I. Schur, Ueber zwei Atten von Faktorenfolgen in der Theorie der algebraischen Gleichungen,Journal fuer die reine und angewandte Mathematik, Vol. 144, 1914, pp. 89–113.

    MATH  Google Scholar 

  11. G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Vols. 1 and 2, Berlin, 1925.

  12. O. Szász, Inequalities concerning ultraspherical polynomials and Bessel functions,Proceedings of the American Mathematical Society, Vol. 1, 1950, pp. 256–267.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Szegö, Orthogonal polynomials,American Mathematical Society, Colloquium Publications, Vol. 23, second edition, New York 1959.

  14. G. Szegö, On an inequality of P. Turán concerning Legendre polynomials,Bulletin of the American Mathematical Society, Vol. 54, 1948, pp. 401–405.

    Article  MATH  MathSciNet  Google Scholar 

  15. M. Weber and A. Erdélyi, On the finite difference analogue of Rodrigues formula,American Mathematical Monthly, Vol. 59, 1952, pp. 163–168.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

To Paul Turán on his 50th birthday August 18, 1960

This research was supported by the National Science Foundation Grants NSF-G 9669-G 11296.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karlin, S., Szegö, G. On certain determinants whose elements are orthogonal polynomials. J. Anal. Math. 8, 1–157 (1960). https://doi.org/10.1007/BF02786848

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02786848

Keywords

Navigation