◀ ▲ ▶Branches / Analysis / Proposition: Exponential Function
Proposition: Exponential Function
The exponential series
\[\sum_{n=0}^\infty\frac{x^n}{n!}\]
is an absolutely convergent series for every real number \(x\in\mathbb R\). It defines a function \(\exp:\mathbb R\mapsto \mathbb R\), called the exponential function for all \(x\in\mathbb R\).
\[\exp(x):=\sum_{n=0}^\infty\frac{x^n}{n!},\quad\quad x\in\mathbb R.\]
Table of Contents
Proofs: 1
 Definition: Exponential Function of General Base
 Proposition: Estimate for the Remainder Term of Exponential Function
 Proposition: Functional Equation of the Exponential Function
 Proposition: Continuity of Exponential Function
 Proposition: \(\exp(0)=1\)
 Proposition: Derivative of the Exponential Function
 Proposition: Integral of the Exponential Function
Mentioned in:
Chapters: 1
Corollaries: 2 3 4 5
Definitions: 6 7 8 9 10
Examples: 11
Proofs: 12 13 14 15 16 17 18 19
Propositions: 20 21 22 23 24 25 26 27 28 29 30
Thank you to the contributors under CC BYSA 4.0!
 Github:
