By José Manuel Aroca, Ragnar Buchweitz, Marc Giusti, Michel Merle (Editors)

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**Complex Functions Examples c-2 - Analytic Functions**

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Jd part curve with e. ~ d ~

Hi (take q free points 0q i > O. i The 0 0 = O. i position and h ~ points~ we m e a n and each = ~ ) is the the i = The have with exponent 0 J0 a free the in relationship to t h e p r e c e e d i n 9 it an of in the Puiseux series. is Here b y characteristic indetermination. ~ have a [1] until the partial sum branches Then in in the unity. In way that root of such a is a. -th J y' y' point series ~-1' corresponding is a.. c~J through series OJi' j=O, . . , which point determined~ coefficient O.

Of a m a t r i x desingularization projection embedding of expansion, irreducible preserving process expansion algebroid a Hamburger-Noether for means sequence space computation, a given by considered orig n curve. In this some are desi ngularization a Hamburger-Noether information of t h e the expansions minimum a d-plane, coordinate integer on multiplicity of is the d for to which Furthermore with in f a c t , d-planes way a d-plane sequence. 0" a g r e e s and, result in a n a t u r a l a projection sequence to d e t e r m i n e that for provides of a any a generic projection.