A general formalism of the angular distribution of emitted electrons in the bound muon decay is made in terms of the multi pole series of the relativistic electron wave functions. The effect of the finite size nucleus to wave functions is properly taken into account for the bound muon and emitted electron. In order to show the importance of this effect, energy spectra and asymmetry coefficients are given numerically in the cases of 160, 40Ca, 90Zr and 2°"Pb. § 1. Introduction Recent development of experimental facilities has made it possible to produce high-intensity muon beams available for studying various fields of physics. In nuclear physics there have been increasing interests in polarization phenomena due to the muon capture in complex nuclei. These are asymmetric distribution of neutrons after the muon capture, I) nuclear polarization of the daughter nucleV) asymmetry of y-rays in radiative capture, etc. 3 ) In atomic physics there are also a number of publications. Two of them are referred to here on the depolarization of bound muons due to the spin-orbit interactions and hyperfine interactions between muon and nucleus,4),5) and the repolarization of bound muons due to hyperfine interactions of muon with Bi. Because of its large spin, Bi is strongly polarized by the internal magnetic field of ferromagnetic compounds BiMn.6) In these studies it is very important to have accurate information on the degree of muon polarization in the 1s1/2 state of muonic atoms experimentally.In the muon decay, the emitted electron is distributed asymmetrically with respect to the muon polarization axis because of parity nonconservation. Therefore, the muon polarization in the 1s1/2 state of a muonic atom is deterinined by measuring the asymmetric distribution of electrons in the bound muon decay. Since the measured electron asymmetry is described by a product of the muon polarization and the asymmetry parameter, it is indispensable to know a theoretical value of the asymmetry parameter in the bound muon decay in order to extract the muon polarization from the measured electron asymmetry accurately. The asymmetry parameter is supposed to be different from that in the free muon decay. Until now this difference is, however, not fully clarified yet.In the early 1950's, Porter and PrimakoW) first pointed out that the decay rate and the electron energy spectrum in the bound muon decay are quite different from those in the free muon decay. Later, there appeared several works on these problems. B
)-Il)Huff 9 ) and Hanggi et al. lO ) calculated the electron energy spectrum in heavy muonic atoms accurately, where they expanded electron wave functions into partial waves and took the nuclear finite size effect into account.On the other hand there were only two publications on the electron angular