  A method for reducing Feynman integrals, depending on several kinematic
variables and masses, to a combination of integrals with fewer variables is
proposed. The method is based on iterative application of functional equations
proposed by the author. The reduction of the one-loop scalar triangle and box
integrals with massless internal propagators to simpler integrals is described
in detail. The triangle integral depending on three variables is represented as
a sum over three integrals depending on two variables. By solving the
dimensional recurrence relations for these integrals, an analytic expression in
terms of the $_2F_1$ Gauss hypergeometric function and the logarithmic function
was derived.
  By using the functional equations, the one-loop box integral with massless
internal propagators, which depends on six kinematic variables, was expressed
as a sum of 12 terms. These terms are proportional to the same integral
depending only on three variables different for each term. For this integral
with three variables, an analytic result in terms of the $F_1$ Appell and
$_2F_1$ Gauss hypergeometric functions was derived by solving the recurrence
relation with respect to the spacetime dimension $d$. The reduction equations
for the box integral with some kinematic variables equal to zero are
considered.
