# Algebraic logarithmic singular point

An isolated singular point $z _ {0}$ of an analytic function $f(z)$ such that in a neighbourhood of it the function $f(z)$ may be represented as the sum of a finite number of terms of the form

$$( z - z _ {0} ) ^ {-s} [ \mathop{\rm ln} ( z - z _ {0} ) ] ^ {k} g (z) ,$$

where $s$ is a complex number, $k$ is a non-negative integer, and $g(z)$ is a regular analytic function at the point $z _ {0}$ with $g ( z _ {0} ) \neq 0$.

#### References

 [1] L. Bieberbach, "Analytische Fortsetzung" , Springer (1955) pp. Sect. 3
How to Cite This Entry:
Algebraic logarithmic singular point. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Algebraic_logarithmic_singular_point&oldid=45063
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article