A simple method to compute spherical harmonic coefficients for the potential model of the coronal magnetic field

It is impossible to make a direct measurement of the coronal magnetic field from the ground. The coronal magnetic field is, then, usually inferred by extrapolation of the observed photospheric magnetic field. The so-called potential model has been used for this extrapolation. We have to solve the Laplacian equation of the magnetic scalar potential. This magnetic scalar potential can be expanded into a spherical harmonic series. In this paper, new simple recursion formulae are proposed to solve the Laplacian equation; that is, to determine the spherical harmonic coefficients.