  The muon spin relaxation method ({\mu}SR) is a powerful microscopic tool to
probe electronic states of materials observing local magnetic field
distributions on the muon. It often happens that a distribution of local
magnetic fields shows intermediate state between Gaussian and Lorentzian
shapes. In order to generally describe intermediate field distributions, we
dealt the convolution of two isotropic distributions in the three dimension and
derived exact muon-spin relaxation functions which can be applied to all
crossover regimes between the Gaussian and Lorentzian.
