, the principal part
has several independent meanings.
of the Laurent series
of a function f
is the series of terms with negative degree, that is
If f(z) has an essential singularity at p, then the principal part is an infinite sum, and vice versa.
Consider the difference between the function differential
and the actual increment:
The differential dy
is the principal (linear) part
of the function increment Δy
The term principal part
is used for certain kinds of distribution having a singular support
at a single point.