Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

The method for obtaining functional equations, recently proposed by one of the authors [O.V. Tarasov, Phys. Lett. B 670 (2008) 67, arXiv:0809.3028 [hep-ph]], is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representations is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation.