The Laurent series of the complex logarithm function log z represents the logarithm as an infinite sum of terms with both positive and negative powers of z. This series expression captures the behavior of log z in the vicinity of singularities, known as branch points or branch cuts. The principal part of the Laurent series includes terms with negative powers and describes the logarithmic singularity at z = 0, while the regular part consists of terms with positive powers and converges for values of z that satisfy certain conditions.
