Re: New Complex Book!

On 24-11-2008 6:15, Denis Feldmann wrote:

I like your formulation of Rouche's theorem: The condition |f(z)-g(z)|< |f(z)| + |g(z)| is
symmetrical and
easier to remember than the traditional one.

Strange : this is the way it is written in the French Wikipedia (and the way I learned it), but not in the English one (which only mentions the traditional one). Perhaps, as often, it was the original version ?

No. The original version (published in 1910) was this: if the domain of
two holomorphic functions _f_ and _g_ contain a closed disk B and if,
for some number _a_, the inequality |a f(z)/g(z)| < 1 holds at the
boundary of the disk, then the equations g(z) - a f(z) = 0 and g(z) = 0
have the same number of roots in B.

I took this information from Remmert's book Theory of Complex Functions,
where it is also stated that the symmetrical version appeared in 1962.

Best regards,

Jose Carlos Santos
.

Relevant Pages

  • Re: Entire function
    ... Best regards, ... Jose Carlos Santos ... Edgar probably meant to say `In English, ...
    (sci.math)
  • Re: Entire function
    ... In English, h is an analytic function. ... Best regards, ... Jose Carlos Santos ...
    (sci.math)
  • Re: T^-1(T(U)) = ?
    ... T does not have an inverse map. ... Best regards, ... Jose Carlos Santos ... not know how correct called in english. ...
    (sci.math)
  • Re: So is Australia raping the Pacific, too?
    ... or anybody else couldn't play highly paid club rugby anywhere in the ... Who says he can't be Fijian AND Australian? ... Stevens - English Father ... were talking about what nationality a player 'regards himself as'. ...
    (rec.sport.rugby.union)
  • Incorporation of Foreign Ideas/Concepts and Vocabulary in Arabic
    ... Arabic seems to be more hostile to foreign vocabulary than English. ... Initial Hamza is used to solve the problem of consonant clusters ... Are there any other linguistic changes? ... Regards ...
    (sci.lang)
Loading