We report exact analytical results for the energy of the Bose Laughlin state of small systems of electrons at half filling factor of the lowest Landau level. The results apply to a disk geometry and the number of particles in the system consists of up to four electrons immersed in a neutralizing jellium background. Exact calculation of various forms of energy becomes feasible after one transforms all the quantities of interest in terms of Jacobi coordinates. Analytical results of this nature serve as excellent benchmarks to test the accuracy of various computational methods and approaches used in the field.