The function of POLM (DNA polymerase mu, ENSG00000122678) is as follows. Catalyzes template-directed nucleotide addition during gap filling at DNA double-strand breaks (PubMed:10747040, PubMed:10982892, PubMed:12640116, PubMed:12888504, PubMed:17483519, PubMed:17915942, PubMed:26240373). Functions as a gap-filling polymerase involved in repair of DNA double-strand breaks by non-homologous end joining (NHEJ) (PubMed:12640116, PubMed:17915942, PubMed:26240373). Displays reduced sugar discrimination, incorporating deoxyribonucleotides and ribonucleotides with similar efficiency on DNA primer strands, and is able to polymerize nucleotides on RNA-terminated primer strands in vitro (PubMed:12640116, PubMed:12888504). Participates in immunoglobulin (Ig) light chain gene rearrangement in V(D)J recombination (By similarity). {ECO:0000250|UniProtKB:Q9JIW4, ECO:0000269|PubMed:10747040, ECO:0000269|PubMed:10982892, ECO:0000269|PubMed:12640116, ECO:0000269|PubMed:12888504, ECO:0000269|PubMed:17483519, ECO:0000269|PubMed:17915942, ECO:0000269|PubMed:26240373}.