  The radial distribution of luminous L_X>10^{36} erg/s X-ray point sources in
the bulge of M31 is investigated using archival Chandra observations. We find a
significant increase of the specific frequency of X-ray sources, per unit
stellar mass, within 1 arcmin from the centre of the galaxy. The radial
distribution of surplus sources in this region follows the density squared law,
suggesting that they are low-mass X-ray binaries formed dynamically in the
dense inner bulge. We investigate dynamical formation of LMXBs, paying
particular attention to the high velocity regime characteristic for galactic
bulges, which has not been explored previously. Our calculations suggest that
the majority of the surplus sources are formed in tidal captures of black holes
by main sequence stars of low mass, M<0.3-0.4 M_sol, with some contribution of
NS systems of same type. Due to the small size of the accretion discs a
fraction of such systems may be persistent X-ray sources. Some of sources may
be ultra-compact X-ray binaries with helium star/white dwarf companions. We
also predict a large number of faint transients, both NS and BH systems, within
1 arcmin from the M31 galactic centre. Finally, we consider the population of
dynamically formed binaries in Galactic globular clusters, emphasizing the
differences between these two types of stellar environments
