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Transcendental branch point

From Encyclopedia of Mathematics
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of an analytic function

A branch point that is not an algebraic branch point. In other words, it is either a branch point of finite order at which, however, there does not exist a finite or infinite limit

or a logarithmic branch point of infinite order. For example, the first possibility is realized at the transcendental branch point for the function , the second for the function .

In the first case the function can be expanded in a neighbourhood of in the form of a Puiseux series

with an infinite number of non-zero coefficients with negative indices.

References

[1] A.I. Markushevich, "Theory of functions of a complex variable" , 2 , Chelsea (1977) (Translated from Russian)
How to Cite This Entry:
Transcendental branch point. E.D. Solomentsev (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Transcendental_branch_point&oldid=12387
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098