  New integral representations for the Adler D-function and the R-ratio of the
electron-positron annihilation into hadrons are derived in the general
framework of the analytic approach to QCD. These representations capture the
nonperturbative information encoded in the dispersion relation for the
D-function, the effects due to the interrelation between spacelike and timelike
domains, and the effects due to the nonvanishing pion mass. The latter plays a
crucial role in this analysis, forcing the Adler function to vanish in the
infrared limit. Within the developed approach the D-function is calculated by
employing its perturbative approximation as the only additional input. The
obtained result is found to be in reasonable agreement with the experimental
prediction for the Adler function in the entire range of momenta $0 \le Q^2 <
\infty$.
