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Logarithmic Singularity


LogarithmicSingularity

A logarithmic singularity is a singularity of an analytic function whose main z-dependent term is of order O(lnz). An example is the singularity of the Bessel function of the second kind

 Y_0(z)∼(2gamma)/pi+2/piln(1/2z)+...

at z=0 (where gamma is the Euler-Mascheroni constant), plotted above along the real axis, where Y_0(z) is shown in red and the constant and logarithmic terms shown in blue.

Singularities with leading term consisting of nested logarithms, e.g., lnlnlnz, are also considered logarithmic.

A logarithmic singularity is equivalent to a logarithmic branch point.


See also

Logarithmic Branch Point, Singularity

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Cite this as:

Weisstein, Eric W. "Logarithmic Singularity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogarithmicSingularity.html

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