Re: Ping: Jose Carlos Santos

Dave L. Renfro wrote:

I was sorting through some papers this morning and came
across your paper, co-authored with Gabriela Chaves,
"Why some elementary functions are not rational"
(Mathematics Magazine 77, 2004, 225-226). If you're
interested, the following references also deal with
various aspects of this topic. In particular, Speck
proves that each of the elementary transcendental
functions (trigonometric, exponential, and their
inverses) differs from every algebraic function on
every open interval.

Thanks. I will look at them. The paper by Speck should be interesting; I
certainly would like to see how he deals with the logarithm.

Godfrey Harold Hardy, A COURSE OF PURE MATHEMATICS,
9'th edition, Cambridge University Press, 1947. [see pp. 52-57]

Concerning this one, since I owe a copy of the 10th edition, could you
please provide the section number(s) instead?

James Pierpont, THE THEORY OF FUNCTIONS OF REAL VARIABLES,
Volume 1, Ginn and Company, 1905. [see pp. 123-137]
http://historical.library.cornell.edu/math/math_P.html

This link doesn't seem to be working.

Thanks for your interest.

Best regards,

Jose Carlos Santos
.

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