Skip to main content
Log in

Eine Bemerkung über die Charakterisierung der „klassischen” orthogonalen Polynome

  • Published:
Acta Mathematica Academiae Scientiarum Hungarica Aims and scope Submit manuscript

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.

Literaturverzeichnis

  1. T. J. Stieltjes,Oeuvres completes (Groningen, 1914), S. 432–439.

  2. V. Romanovski, Sur quelques classes nouvelles des polynomes orthogonaux,Comptes Rendus Acad. Sci., Paris,188 (1929), S. 1023–1025.

    MATH  Google Scholar 

  3. S. Bochner, Über Sturm-Liouville Polynomsysteme,Math. Zeitschr.,29 (1929), S. 720–736.

    MATH  Google Scholar 

  4. J. Chokhate (Shohat), Sur une classe étendue de fractions continues algébriques et sur les polynomes de Tchebycheff correspondents,Comptes Rendus Acad. Sci., Paris,191 (1930), S. 989–990.

    MATH  Google Scholar 

  5. E. H. Hildebrandt, Systems of polynomials connected with the Pearson differential and difference equations,Bulletin Amer. Math. Soc.,37 (1931), S. 676.

    MATH  Google Scholar 

  6. E. H. Hildebrandt, Systems of polynomials connected with the Charlier expansions and the Pearson differential and difference equation,Annals of Math. Stat. 2 (1931), S. 379–439.

    Article  MATH  Google Scholar 

  7. M. Marden, A rule of signs involving certain orthogonal polynomials,Annals of Math.,33 (1932), S. 118–124.

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Abramesco, Les polynomes orthogonaux,Annales Fac. Sci. Univ. Toulouse, (3),24 (1932), S. 67–87.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Shohat (Chokhate), Théorie générale des polynomes orthogonaux de Tchebycheff,Mémorial des Sci. Math.,66 (Paris, 1934), insb. S. 15–18 und S. 31–36.

    Google Scholar 

  10. J. Meixner, Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion,Journal London Math. Soc.,9 (1934), S. 6–13.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. Hahn, Über die Jacobischen Polynome und zwei verwandte Polynomklassen,Math. Zeitschr.,39 (1935), S. 634–638.

    Article  MATH  Google Scholar 

  12. H. L. Krall, On derivatives of orthogonal polynomials,Bulletin Amer. Math. Soc.,42, (1936), S. 423–428.

    Article  MathSciNet  MATH  Google Scholar 

  13. H. L. Krall, On higher derivatives of orthogonal polynomials,Bulletin Amer. Math. Soc.,42 (1936), S. 867–870.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Koulik, Les polynomes orthogonaux en connection avec certaines schémes de distributions discrétes de probabilités,J. Inst. Math. Acad. Sci. Ukraine,1 (1937), S. 89–136.

    MATH  Google Scholar 

  15. M. S. Webster, Orthogonal polynomials with orthogonal derivatives,Bulletin Amer. Math. Soc.,44 (1938), S. 880–888.

    Article  MathSciNet  MATH  Google Scholar 

  16. W. Hahn, Über höhere Ableitungen von Orthogonalpolynomen,Math. Zeitschr.,43 (1938), S. 101.

    Article  MATH  Google Scholar 

  17. C. E. Dieulefait, Die Momente einer Gruppe von Wahrscheinlichkeitsfunktionen und ihre Beziehungen zu den linearen Differentialgleichungen zweiter Ordnung, den Gleichungen von Laplace, den algebraischen Kettenbrüchen und den Summen divergenter Reihen,An. Soc. Ci. Argentina,125 (1938), S. 81–111.

    MATH  Google Scholar 

  18. J. Shohat, A differential equation for orthogonal polynomials,Duke Math. Journal,5 (1939), S. 401–417.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Shohat, E. Hille, J. L. Walsh, A Bibliography on orthogonal polynomials,Bull. of the Nat. Res. Council,103 (Washington, 1940).

  20. F. S. Beale, On a certain class of orthogonal polynomials,Annals of Math. Stat.,12 (1941), S. 97–103.

    Article  MathSciNet  MATH  Google Scholar 

  21. D. Jackson,Fourier-series and orthogonal polynomials, Carus Monograph 6 (Oberlin, Ohio, 1941), Ch. VI, VII. 10.

  22. H. L. Krall, On derivatives of orthogonal polynomials. II,Bulletin Amer. Math. Soc.,47 (1941), S. 261–264.

    Article  MathSciNet  MATH  Google Scholar 

  23. F. Simonart, Sur les systémes de polynomes de Sturm-Liouville,Acad. Roy. Belg., Cl. Sci., (5),33 (1947), S. 8–21.

    MathSciNet  Google Scholar 

  24. W. Hann, Über Orthogonalpolynome, dieq-Differenzengleichungen genügen,Math. Nachrichten,2 (1949), S. 4–34.

    Article  Google Scholar 

  25. И. П. Натансон, Конструктивная теория функций (Москва-Ленинград, 1949), §§ VI. 1, 2, VIII. 3, 4.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aczél, J. Eine Bemerkung über die Charakterisierung der „klassischen” orthogonalen Polynome. Acta Mathematica Academiae Scientiarum Hungaricae 4, 315–321 (1953). https://doi.org/10.1007/BF02127589

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02127589

Navigation