Recently, the O(alpha) and O(alpha(3) ln alpha) radiative corrections to the orthopositronium lifetime have been presented in closed analytical form, in terms of basic irrational numbers that can be evaluated numerically to arbitrary precision {[}B. A. Kniehl, A. V. Kotikov, and O. L. Veretin, Phys. Rev. Lett. 101, 193401 (2008)]. Here, we present the details of this calculation and reveal the nature of these new constants. We also list explicit transformation formulas for generalized polylogarithms of weight four, which may be useful for other applications.