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The article is devoted to the practical material on expansions andmean-square approximations of specific iterated Ito and Stratonovich stochasticintegrals of multiplicities 1 to 6 with respect to components of themultidimensional Wiener process on the base of the method of generalizedmultiple Fourier series. More precisely, we used the multiple Fourier--Legendreseries converging in the sense of norm in the space $L_2([t, T]^k)$$(k=1,\ldots,6)$ for approximation of iterated Ito and Stratonovich stochasticintegrals. The considered iterated Ito and Stratonovich stochastic integralsare part of the stochastic Taylor expansions (Taylor-Ito andTaylor-Stratonovich expansions). Therefore, the results of the article can beuseful for construction of the high-order strong numerical methods for Itostochastic differential equations. Expansions of iterated Ito and Stratonovichstochastic integrals of multiplicities 1 to 6 using Legendre polynomials arederived. The convergence with probability 1 of the mentioned method ofgeneralized multiple Fourier series is proved for iterated Ito stochasticintegrals of multiplicities $k$ $(k\in\mathbb{N})$ for the cases of multipleFourier-Legendre series and multiple trigonometric Fourier series.

Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic  Integrals of Multiplicities 1 to 6 from the Taylor-Ito and  Taylor-Stratonovich Expansions Using Legendre Polynomials