  We study the semirelativistic Hamiltonian operator composed of the
relativistic kinetic energy and a static harmonic-oscillator potential in three
spatial dimensions and construct, for bound states with vanishing orbital
angular momentum, its eigenfunctions in compact form, i. e., as power series,
with expansion coefficients determined by an explicitly given recurrence
relation. The corresponding eigenvalues are fixed by the requirement of
normalizability of the solutions.
