Difference between revisions of "Algebraic logarithmic singular point"
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| − | + | 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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> L. Bieberbach, "Analytische Fortsetzung" , Springer (1955) pp. Sect. 3</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> L. Bieberbach, "Analytische Fortsetzung" , Springer (1955) pp. Sect. 3</TD></TR></table> | ||
Latest revision as of 16:10, 1 April 2020
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
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