On the completeness of the system of weber functions

Huseynov H. M., Abbasova K. E.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.41, no.4, pp.90-94, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 4
  • Publication Date: 2021
  • Journal Name: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.90-94
  • Keywords: Completeness of a system of functions, Eigenvalues, Perturbed harmonic oscillator, Weber function
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

(√ ) Abstract. Weber functionsD λn−12x, n= 0,1,2, …, are considered, where λn is the eigenvalue of 2 the perturbed harmonic oscillator on the semi-axis with finite potential and with the Dirichlet boundary { condition at zero. The completeness in the space L2 (0, ∞) of a system of functions is proved. D λn−1 2 (√ 2x )}∞ n=0.