On the issue of expansion of a given function in a series of Jacobi polynomials
Authors:
Abstract
The purpose of this note is to simplify the method proposed by Academician N. M. Krylov for expanding a given function in a series in Jacobi polynomials. By constructing a priori an expansion with uniform and absolute convergence, we show, without relying on the Riesz-Fischer theorem, that it can be identified with expansions in Jacobi polynomials.
Область исследования:
(Archived) Articles
Funding:
None
References
- V. A. Steklov. Journal für reine und angewandte Mathematik, vol. 125 (1903), p. 214.
- Zapiski Petersburgskoi Academii Nauk, vol. XV, No. 7 (1904), p. 20. (in Russian)
- N. M. Krylov. Comptes rendus des séances de l'Académie des Sciences, Paris, vol. 150 (1910), p. 316.
- Izvestia Kievskogo Universiteta (1910), No. 10. (in Russian)
- N. M. Krylov. On Expansions in Series in Fundamental Functions... and on Expansions in Lubbie Polynomials. Dissertation, Kiev (1911), pp. 94–103. (in Russian)
- Encyclopédie des Sciences mathématiques (French edition), vol. 2, no. 5, fasc. 2 (1914), p. 234.
- Comptes rendus, vol. 144 (1907), pp. 615 and 1022.
- R. Appell. Archiv der Mathematik und Physik, vol. 66 (1881), p. 238.
Similar articles
Magnetic field of electromagnetic separators M. V. N. 6 (with ring magnets) and M. D. 4 (with reversing magnetic poles) and the theory of calculation of electromagnetic systems of separators of these types
1934 A. Ya. Sochnev
Parasitic craters that appeared emerged in 1932 at the foot of the Klyuchevskoi volcano in Kamchatka
1934 V. S. Kulakov