Jump to navigation Jump to search
Let $a$ be a non-zero algebraic number (possibly complex).
- $e^a$ is transcendental
where $e$ is Euler's number.
Let $a$ be a algebraic number (possibly complex) which is neither $0$ nor $1$.
- any value of $\ln a$ is transcendental
where $\ln$ denotes complex natural logarithm.
This follows trivially from Hermite-Lindemann-Weierstrass Theorem by taking $n = 1$.
Source of Name
This entry was named for Charles Hermite, Carl Louis Ferdinand von Lindemann and Karl Theodor Wilhelm Weierstrass.