# Algebraic logarithmic singular point

From Encyclopedia of Mathematics

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