[en] The radial equation of a static massive scalar meson field in a Schwarzschild background space is solved by asymptotic methods leading to solutions over the whole range. The approach is used to obtain the form of the Yukawa potential in the presence of a large Schwarzschild black hole, and to show that the meson field fades away to zero as the event horizon is reached, in agreement with the 'no hair' conjecture. (author)