Ping: Jose Carlos Santos

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.

George P. Speck, "Elementary transcendental functions",
Mathematics Magazine 42 (1969), 200-202.

Reprinted on pp. 80-82 of "A Century of Calculus: Part II
1969-1991", The Mathematical Association of America, 1992.

Richard Wesley Hamming, "An elementary discussion of the
transcendental nature of the elementary functions", American
Mathematical Monthly 77 (1970), 294-297.

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

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

Dave L. Renfro

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