When a zero isn't zero (math quote) - sci.math

Message from discussion When a zero isn't zero (math quote)

Remcheese

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More options Nov 5 2009, 12:31 am

Newsgroups: sci.math

From: "Remcheese" <nos...@spamless.com>

Date: Wed, 4 Nov 2009 18:31:43 -0600

Local: Thurs, Nov 5 2009 12:31 am

Subject: Re: When a zero isn't zero (math quote)

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"Tonico" <Tonic...@yahoo.com> wrote in message

news:b9a7111f-815d-4dad-9ad3-95cc0f77cb6f@m16g2000yqc.googlegroups.com...
On Nov 4, 9:14 pm, "Dave L. Renfro" <renfr...@cmich.edu> wrote:

> O-K, this may be a well-known folklore math quote,
> but a google-web search gives only 2 hits (both being
> the same book) and a google-book search gives only
> 7 hits (5 essentially different items, one of which
> is the google-web hit I got):

> "A zero of order zero is a regular point at which the
> function is not zero."

> I saw this in Pi Mu Epsilon Journal [Volume 2, Number 5
> (Fall 1956), p. 224], where it's followed with "(From a
> book on complex variables.)" From the google-book hits
> it appears the original source is Volume 1 of Knopp's
> "Theory of Functions".

> Dave L. Renfro

Indeed. It is a foot note in page 90 in the 1st american edition of
Knopp's book, 1945.

Tonio

The entire footnote says;

" If f(z) is regular at Zo and f(Zo) not equal to a, it is often convenient
to call the pont Zo an a-point of order zero. A zero of order zero is a
regular point at which the function is not zero."

and it is under
Definition. A point Zo of a region of regularity of the function f(Z) is
called a zero of the function if f(Zo) = 0. In general, if f(Zo) = a, Zo is
called an a-point of f(Z).

[read Zo as Z sub zero)

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