e/Characterizations of the exponential function

Information
has gloss	eng: In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other. As a special case of these considerations, we will see that the three most common definitions given for the mathematical constant e are also equivalent to each other.
lexicalization	eng: Characterizations of the exponential function
instance of	(noun) a function in which an independent variable appears as an exponent exponential function, exponential