Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On Appell polynomials

  • 85 Accesses

  • 6 Citations

Abstract

Necessary and sufficient conditions are found for which a sequence of Appell polynomials forms a quasipower basis in ∀ A(¦z¦<R),0<R<+∞.

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

Literature cited

  1. 1.

    S. N. Bernshtein, Collected Papers, Volume 2 [in Russian], Moscow (1954).

  2. 2.

    V. B. Ozhegov, “On certain extremal properties of generalized Appell polynomials,” Dokl. Akad. Nauk SSSR,159, No. 5, 985–987 (1967).

  3. 3.

    V. B. Ozhegov, “On generalized Appell polynomials,” in: Investigations in Modern Problems of the Constructive Theory of Functions [in Russian], 595–601, Baku (1965).

  4. 4.

    Yu. A. Kaz'min, “On expansions in series of Appell polynomials,” Matem. Zametki,5, No. 5, 509–520 (1969).

  5. 5.

    M. G. Khaplanov, Linear Operators in an Analytic Space and Their Applications [in Russian], Doctoral Dissertation, Rostov-on-Don (1960); Author's Abstract published in Kharkov in 1960.

  6. 6.

    S. Banach, Course in Functional Analysis [Ukrainian translation], Kiev (1948).

  7. 7.

    B. Ya. Levin, Distribution of the Roots of Integral Functions [in Russian], Moscow (1954).

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 6, No. 2, pp. 161–172, August, 1969.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kaz'min, Y.A. On Appell polynomials. Mathematical Notes of the Academy of Sciences of the USSR 6, 556–562 (1969). https://doi.org/10.1007/BF01093697

Download citation