We present an analytical formula for the Bose-Einstein correlations (BEC) which includes effects of both Coulomb and strong final stateinteractions (FSI). It was obtained by using Coulomb wave function together with the scattering partial wave amplitude of the strong interactions describing data on the $s$-wave phase shift. We have proved numerically that this method is equivalent to solving Schr{o}dinger equation with Coulomb and the $s$-wave strong interaction potentials. As an application we have analysed, using our formula which includes the degree of coherence and the long range correlation, the data for $e^+e^-$ annihilations. We have found that the degree of coherence present in our formula approaches approximately unity whereas the long range correlation parameter becomes approximately zero. These results suggest that the physical meanings of the fractional degree of coherence and the long range correlation observed in various other analyses can most probably be attributed to FSI.
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