×

zbMATH — the first resource for mathematics

Eine Bemerkung über die Charakterisierung der “klassischen” orthogonalen Polynome. (German. Russian summary) Zbl 0051.30401

PDF BibTeX XML Cite
Full Text: DOI
References:
[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. · JFM 55.0915.03
[3] S. Bochner, Über Sturm-Liouville Polynomsysteme,Math. Zeitschr.,29 (1929), S. 720–736. · JFM 55.0260.01
[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. · JFM 56.0946.01
[5] E. H. Hildebrandt, Systems of polynomials connected with the Pearson differential and difference equations,Bulletin Amer. Math. Soc.,37 (1931), S. 676.
[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. · Zbl 0004.34402 · doi:10.1214/aoms/1177732950
[7] M. Marden, A rule of signs involving certain orthogonal polynomials,Annals of Math.,33 (1932), S. 118–124. · JFM 58.0112.02 · doi:10.2307/1968104
[8] N. Abramesco, Les polynomes orthogonaux,Annales Fac. Sci. Univ. Toulouse, (3),24 (1932), S. 67–87. · JFM 58.0379.01 · doi:10.5802/afst.371
[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.
[10] J. Meixner, Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion,Journal London Math. Soc.,9 (1934), S. 6–13. · JFM 60.0293.01 · doi:10.1112/jlms/s1-9.1.6
[11] W. Hahn, Über die Jacobischen Polynome und zwei verwandte Polynomklassen,Math. Zeitschr.,39 (1935), S. 634–638. · Zbl 0011.06202 · doi:10.1007/BF01201380
[12] H. L. Krall, On derivatives of orthogonal polynomials,Bulletin Amer. Math. Soc.,42, (1936), S. 423–428. · Zbl 0014.39903 · doi:10.1090/S0002-9904-1936-06323-8
[13] H. L. Krall, On higher derivatives of orthogonal polynomials,Bulletin Amer. Math. Soc.,42 (1936), S. 867–870. · Zbl 0016.01905 · doi:10.1090/S0002-9904-1936-06451-7
[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.
[15] M. S. Webster, Orthogonal polynomials with orthogonal derivatives,Bulletin Amer. Math. Soc.,44 (1938), S. 880–888. · Zbl 0020.01303 · doi:10.1090/S0002-9904-1938-06896-6
[16] W. Hahn, Über höhere Ableitungen von Orthogonalpolynomen,Math. Zeitschr.,43 (1938), S. 101. · JFM 63.0316.01 · doi:10.1007/BF01181087
[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. · JFM 64.1085.04
[18] J. Shohat, A differential equation for orthogonal polynomials,Duke Math. Journal,5 (1939), S. 401–417. · JFM 65.0285.03 · doi:10.1215/S0012-7094-39-00534-X
[19] J. Shohat, E. Hille, J. L. Walsh, A Bibliography on orthogonal polynomials,Bull. of the Nat. Res. Council,103 (Washington, 1940). · Zbl 0025.04103
[20] F. S. Beale, On a certain class of orthogonal polynomials,Annals of Math. Stat.,12 (1941), S. 97–103. · Zbl 0024.39501 · doi:10.1214/aoms/1177731789
[21] D. Jackson,Fourier-series and orthogonal polynomials, Carus Monograph 6 (Oberlin, Ohio, 1941), Ch. VI, VII. 10. · Zbl 0060.16910
[22] H. L. Krall, On derivatives of orthogonal polynomials. II,Bulletin Amer. Math. Soc.,47 (1941), S. 261–264. · Zbl 0024.39402 · doi:10.1090/S0002-9904-1941-07427-6
[23] F. Simonart, Sur les systémes de polynomes de Sturm-Liouville,Acad. Roy. Belg., Cl. Sci., (5),33 (1947), S. 8–21.
[24] W. Hann, Über Orthogonalpolynome, dieq-Differenzengleichungen genügen,Math. Nachrichten,2 (1949), S. 4–34. · Zbl 0031.39001 · doi:10.1002/mana.19490020103
[25] И. П. Натансон, Конструктивная теория функций (Москва-Ленинград, 1949), §§ VI. 1, 2, VIII. 3, 4. · Zbl 1200.90003
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.