Context :

Aims : We explore the population of X-ray point sources in the bulge of M31 to contrast properties of various subpopulations , such as persistent and transient sources and primordial LMXBs and dynamically formed ones .

Methods : Based on the data from 26 archival Chandra observations we study the source content and properties of various subpopulations of X-ray sources to a maximum distance of 12′ from the centre of M31 .

Results : To a limiting luminosity of \sim 10 ^ { 35 } erg s ^ { -1 } we find 263 X-ray point sources , with \sim 1 / 3 of these being background galaxies .
A study of the spatial distribution and the luminosity function of the X-ray sources shows that the distribution of primordial LMXBs is consistent with the distribution of the K -band light and that their luminosity function flattens below \sim 10 ^ { 37 } erg s ^ { -1 } to the dN / dL \propto L ^ { -1 } law in agreement with the behaviour found earlier for LMXBs in the Milky Way and in Cen A .
Within a radius of 12 \arcmin , the luminosity function is independent of distance to the centre of M31 , in contrast to earlier Chandra studies .
The LMXBs located in globular clusters and within \sim 1 \arcmin from the centre of M31 are presumably created via dynamical interactions .
The dynamical origin of the r < 1 \arcmin sources is strongly suggested by their radial distribution which follows the \rho ^ { 2 } _ { \textit { * } } profile rather than the K-band light distribution .
Their luminosity function shows a prominent fall-off below \log ( L _ { X } ) \la 36.5 .
Although the statistics is insufficient to claim a genuine low-luminosity cut-off in the luminosity function , the best fit powerlaw with a slope of -0.6 \pm 0.2 is significantly flatter than the dN / dL \propto L ^ { -1 } law .
We also searched for transients and found 28 sources that varied by a factor larger than 20 .
Their spatial distribution follows the distribution of the persistent LMXBs within the accuracy allowed by the limited number of transients .

Conclusions :