Re: The Definition of 'Analytic Function'
From: Jose Capco (jcapco_at_yahoo.com)
Date: 06/16/04
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Date: 15 Jun 2004 23:51:06 -0700
Unfortunately it did not make your question any clearer, it is rather
confusing. I have never seen the term "analytic" being used in such
manner, sometimes one says "can be analytically solved" .. etc. But I
think you must take caution in the usage of "analytic" and not just
say "a function is analytic" if thats what you mean (you didnt mean a
function in fact, but an equation) it might confused people.
> (I'll write ~analytic to differentiate its accepted use from mine)
> Sorry. I was talking too loosely. In fact I should not be talking about
> functions at all, but general equations. For example, x^2 + y^2 = 1 is not
> a function, but I would consider it to be ~analytic. When discussing my
> thinking on ~analytic equations I'm referring to the process of calculating
> the result of f(c) for some constant c. For example, if f(x_{i+1}) = x_i +
> 1, I would call that ~analytic for any initial x_0 in R. However if
> f(x_{i+1}) = x_i + a * x_i * (1 - x_i), then I wouldn't call that ~analytic
> ('a' a constant) except for specific values of a and x_0. I can't in
> general statically solve f(x_2300) without knowing the results for
> f(x_2299), etc... A continuous example would be solving the equation for a
> driven damped pendulum (an equation from physics). Note I'm not restricting
> the term ~analytic to any particular type of equation, but to equations in
> general. (ie: as the term 'continuous mapping' can now be applied to
> non-real and non-complex functions given the term's generalization in
> topology). Hope this is a little clearer.
>
>
>
> l8r, Mike N. Christoff
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