Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well–established method based on a power–series expansions weighted by a Gaussian factor with an adjustable parameter (the so–called Hill–determinant method).