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Vol 8
Pages:
224-226
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RUS
Article

On the issue of expansion of a given function in a series of Jacobi polynomials

Authors:
M. I. Akimov
Date submitted:
1933-07-23
Date accepted:
1933-09-28
Date published:
1934-01-01

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

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References

  1. V. A. Steklov. Journal für reine und angewandte Mathematik, vol. 125 (1903), p. 214.
  2. Zapiski Petersburgskoi Academii Nauk, vol. XV, No. 7 (1904), p. 20. (in Russian)
  3. N. M. Krylov. Comptes rendus des séances de l'Académie des Sciences, Paris, vol. 150 (1910), p. 316.
  4. Izvestia Kievskogo Universiteta (1910), No. 10. (in Russian)
  5. N. M. Krylov. On Expansions in Series in Fundamental Functions... and on Expansions in Lubbie Polynomials. Dissertation, Kiev (1911), pp. 94–103. (in Russian)
  6. Encyclopédie des Sciences mathématiques (French edition), vol. 2, no. 5, fasc. 2 (1914), p. 234.
  7. Comptes rendus, vol. 144 (1907), pp. 615 and 1022.
  8. R. Appell. Archiv der Mathematik und Physik, vol. 66 (1881), p. 238.

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