A logarithmic singularity is a singularity of an analytic function whose main -dependent term is of order . An example is the singularity of the Bessel function of the second kind
at (where is the Euler-Mascheroni constant), plotted above along the real axis, where is shown in red and the constant and logarithmic terms shown in blue.
Singularities with leading term consisting of nested logarithms, e.g., , are also considered logarithmic.
A logarithmic singularity is equivalent to a logarithmic branch point.