We study the form of the electrostatic potential created by a hemispherical surface with uniform surface charge density. We specifically consider a “northern” hemispherical surface and try to obtain analytical expressions for the electrostatic potential at an arbitrary point in space. Some compact analytical results are obtained for special cases and an interesting mathematical integral formula is derived as a by-product of the approach. The results suggest that a general expression for the electrostatic potential at an arbitrary point in space, if possible, would be very hard to obtain in compact analytical form.