  The article is devoted to the expansions of iterated Stratonovich stochastic
integrals of multiplicities 1 to 4 on the base of the combined approach of
generalized multiple and iterated Fourier series. We consider two different
parts of the expansion of iterated Stratonovich stochastic integrals. The
mean-square convergence of the first part is proved on the base of generalized
multiple Fourier series that are converge in the sense of norm in Hilbert space
$L_2([t, T]^k),$ $k=1,2,3,4.$ The mean-square convergence of the second part is
proved on the base of generalized iterated Fourier series that are converge
pointwise. At that, we do not use the iterated Ito stochastic integrals as a
tool of the proof and directly consider the iterated Stratonovich stochastic
integrals. The cases of multiple Fourier-Legendre series and multiple
trigonometric Fourier series are considered in detail. The considered
expansions contain only one operation of the limit transition in contrast to
its existing analogues. This property is very important for the mean-square
approximation of iterated stochastic integrals. The results of the article can
be applied to the numerical integration of Ito stochastic differential
equations.
