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Hermite-Lindemann Theorem

The expression

\begin{displaymath}
A_1e^{\alpha_1}+A_2e^{\alpha_2}+A_3e^{\alpha_3}+\ldots,
\end{displaymath}

in which the Coefficients $A_i$ differ from zero and in which the exponents $\alpha_i$ are Algebraic Numbers differing from each other, cannot equal zero.

See also Algebraic Number, Constant Problem, Integer Relation, Lindemann-Weierstraß Theorem


References

Dörrie, H. ``The Hermite-Lindemann Transcendence Theorem.'' §26 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 128-137, 1965.




© 1996-9 Eric W. Weisstein
1999-05-25