  In the main part of the paper, on the basis of contour integration of complex
meromorphic functions whose singularities lie onto an integration contour, in
the first step, a concept of improper integrals absolute existence of
meromorphic functions, as more general one with respect to the concept of
improper integrals convergence (existence), is introduced into analysis. In the
second step, in the case when a modulus of complex parameter tends to infinity,
an interval of improper integrals convergence of parametric meromorphic
functions is defined. In accordance with this, it is shown that the class of
real valued meromorphic functions, whose finitely many isolated singularities
lie onto a real axis segment, may be expanded into Fourier trigonometric
series, separately. At all points of the segment, at which the meromorphic
functions are continuous ones, the Fourier trigonometric series is summable and
its sum is equal to the function values at those points. Finally, that all is
illustrated by two representative examples.
