  The article is devoted to the construction of expansions of iterated
Stratonovich stochastic integrals of fifth and sixth multiplicities based on
the method of generalized multiple Fourier series converging in the sense of
norm in the Hilbert space $L_2([t, T]^k),$ $k\in\mathbb{N}.$ Specifically, we
mainly use multiple Fourier-Legendre series and multiple trigonometric Fourier
series. Recently, expansions of iterated Stratonovich stochastic integrals of
multiplicity $k,$ $k\in\mathbb{N}$ (the case of continuous weight functions and
an arbitrary complete orthonormal system of functions in $L_2([t, T])$) have
been obtained but under one additional assumption (see Theorem 42). The
considered expansions converge in the mean-square sense and contain only one
operation of the limit transition in contrast to its existing analogues.
Expansions of iterated Stratonovich stochastic integrals turned out much
simpler than appropriate expansions of iterated Ito stochastic integrals. We
use expansions of the latter as a tool of the proof of expansions for iterated
Stratonovich stochastic integrals. Iterated Stratonovich stochastic integrals
are the part of the Taylor-Stratonovich expansion for solutions of Ito
stochastic differential equations. That is why the results of the article can
be applied to the numerical integrations of Ito stochastic differential
equations.
