Definition:Exponential Function/Real/Power Series Expansion

Definition

Let $\exp: \R \to \R_{>0}$ denote the (real) exponential function.

The exponential function can be defined as a power series:

$\exp x := \ds \sum_{n \mathop = 0}^\infty \frac {x^n} {n!}$

The number $\exp x$ is called the exponential of $x$.

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$

• Weisstein, Eric W. "Exponential Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExponentialFunction.html