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.
The logarithmic term can also give a logarithmic branch point. Logarithmic growth and branching describe different aspects of the function.
