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".
> 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.
> 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
That book is a 9 on my sale of 1 to 10 where 10 is the hardist. excellent book complex functions, quite difficult, beyond advanced calculus only 142 pages of 4in by 6in pages in vol 1 came out in 1945, Dover has reprinted it, so it is low cost now.
basic theory of functions of one complex variable, at a pace that will allow for the inclusion of some non-elementary topics at the end. Basic Theory: Holomorphic and harmonic functions; conformal mappings; Cauchy's Theorem and consequences; Taylor and Laurent series; singularities; residues; Dirichlet Series such as the Riemann Zeta Function
> 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).
On Wed, 4 Nov 2009 11:14:42 -0800 (PST), "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."
Heh.
The definition also occurs in an exercise in Complex Made Simple, not in those words.
Anyway, an excellent reason to buy the book is that you _can_ find the phrase "non-zero zeroes" there...
>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
David C. Ullrich
"Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to." (John Jones, "My talk about Godel to the post-grads." in sci.logic.)
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