Algebraic Branch Point
المؤلف:
Knopp, K.
المصدر:
Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, Part II
الجزء والصفحة:
pp. 142-143
27-11-2018
1188
Algebraic Branch Point
A branch point whose neighborhood of values wrap around the range a finite number of times 
as their complex arguments 
varies from 0 to a multiple of 
is called an algebraic branch point of order 
. Such points correspond to the point 
under functions of the form 
.
Formally, an algebraic branch point is a singular boundary point of one sheet of a multivalued function about which a finite number 
of distinct sheets hang together like the surface for 
at the origin and for which the domain of values affixed to these 
sheets in a neighborhood of 
, which can be developed in a series of the form
is such that only a finite number (or zero) negative power of 
appear in the expansion (Knopp 1996, Part II, p. 143).
REFERENCES:
Knopp, K. Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, Part II, pp. 142-143, 1996.
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