Geodesic
Polynomial systems of binomial type and the mean value theorem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2024), pp. 34-46 
A. Kh. Ghiyasi; V. N. Chubarikov. Polynomial systems of binomial type and the mean value theorem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2024), pp. 34-46. http://geodesic.mathdoc.fr/item/VMUMM_2024_5_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a description of sequences of polynomials of binomial type is given and new mean-value theorems are proved.

[1] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, M., 1963

[2] Riordan Dzh., Kombinatornye tozhdestva, Nauka, Gl. red. fiz.-mat. lit-ry, M., 1982

[3] Hurwitz A., “Ueber Abel's Verallgemeinerung der binomischen Formel”, Acta Math., 26 (1902), 199–203 | DOI

[4] Touchard J., “Nombres exponentiels et nombres de Bernoulli”, Canad. J. Math., 8 (1956), 305–320 | DOI

[5] Al-Salaam W.A., “Operational expressions for the Laguerre and other polynomials”, Duke Math. J., 31 (1964), 127–142

[6] Mullin R., Rota G.-C., “On the foundations of combinatorial theory: III. Theory of binomial enumeration”, Graph Theory and its Appl., 1970, 168–213

[7] Arkhipov G.I., Chubarikov V.N., Karatsuba A.A., Trigonometric Sums in Number Theory and Analysis, De Gruyter expositions in mathematics, 39, Berlin–N.Y., 2004

[8] Weyl H., “Über die Gleichverteilung der Zahlen mod. Eins”, Math. Ann., 77 (1916), 313–352 | DOI

[9] Vinogradov I.M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980

[10] Hua L.-K., “An improvement of Vinogradov's mean-value theorem and several applications”, Quart. J. Math., 20 (1949), 48–61 | DOI

[11] Postnikov A.G., Izbrannye trudy, FIZMATLIT, M., 2005

[12] Arkhipov G.I., Izbrannye trudy, Izd-vo Orlov. gos. un-ta, Orel, 2013

[13] Karatsuba A.A., Osnovy analiticheskoi teoriii chisel, FIZMATLIT, M., 1983