  The article is devoted to the expansion of iterated Stratonovich stochastic
integrals of arbitrary multiplicity $k$ $(k\in\mathbb{N})$ based on the
generalized iterated Fourier series converging pointwise. The case of
Fourier-Legendre series as well as the case of trigonometric Fourier series are
considered in details. The obtained expansion provides a possibility to
represent the iterated Stratonovich stochastic integral in the form of iterated
series of products of standard Gaussian random variables. Convergence in the
mean of degree $2n$ $(n\in \mathbb{N})$ of the expansion is proved. Some recent
results on the expansion of iterated Stratonovich stochastic integrals of
multiplicities 3 to 6 are given. The results of the article can be applied to
the numerical solution of Ito stochastic differential equations.

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