The exponential function is a function of the form . Euler's number, , is the base of the natural logarithm. Sometimes, in general, the term exponential function can refer to functions of the form , where are constants. The variable here is the base. The function is sometimes denoted when superscripts are inappropriate.

## Definitions

1.The limit definition:

2.The infinite series:

3.The inverse of the natural logarithm, where is the number such that

4.The unique solution to the initial value problem