  The article is devoted to the expansion of iterated Stratonovich stochastic
integrals of second multiplicity into the double series of products of standard
Gaussian random variables. The proof of expansion is based on the application
of double Fourier-Legendre series and double trigonometric Fourier series
summarized by Pringsheim method. The results of the article are generalized to
the case of an arbitrary complete orthonormal system of functions in the space
$L_2([t, T])$ and $\psi_1(\tau), \psi_2(\tau)\in L_2([t, T]).$ The considered
expansion can be applied to the numerical integration of Ito stochastic
differential equations. Some recent results on the expansion of iterated
Stratonovich stochastic integrals of multiplicities 3 to 6 are given.
