# Re: can we find one-way trapdoor funcation family from the theory of calculus

From: Douglas A. Gwyn (DAGwyn_at_null.net)
Date: 11/22/05

```Date: Tue, 22 Nov 2005 00:10:26 GMT

```

Unruh wrote:
> "Douglas A. Gwyn" <DAGwyn@null.net> writes:
> >Expressing the solution to a mathematical problem in terms
> >of standard, well-studied functions is a reasonable approach.
> I am not saying that it is unreasonable. But in fact today it is probably
> irrelevant. In 1850, only a very few functions were tabulated. Calculating
> anything but those was weeks or months worth of effort to even get an idea
> of how the solution went. If you could use functions that had been
> tabulated, you could sketch the solution from your knowledge of those
> tabulated functions. Now, that is no longer true. A sin, an erfi, or the
> solutions to some horrible non-linear equation are all almost equally
> difficult (easy) to calculate. The difference between "elementary" and
> other functions has rapidly disappeared.

Or put another way, what is "elementary" is a matter of convention.

Anyway, recall that the original issues was whether the integral of
exp(x^2) existed, which the o.p. said his instructor had denied, so
we were trying to figure out what the instructor might have meant
(as an alternative to him having been outright wrong, which is also
a possibility). Some of the ideas were that the instructor had
meant *only* when the domain was the whole line (contrary to what
the o.p. had said), or that he had meant that the finite integral
was not expressible as a combination of some presumed set of
"standard" functions, constants, and operations. I brought up Erfi
because not only is it the solution, with well-known proerties that
can be easily looked up, but also in some circles it is fairly
"standard".

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