# Exponential: Difference between revisions

This page describes the monadic arithmetic function. For the dyadic function, see Power (function).
 `*`

Exponential (`*`) is a monadic scalar function which computes the exponential function (i.e. the power of Euler's constant e) of the argument. Exponential shares the glyph `*` with the dyadic arithmetic function Power.

## Examples

Euler's constant itself can be obtained by supplying 1 as the argument.

```      *1
2.718281828
```

On APL implementations that support complex numbers, one can demonstrate Euler's identity (with the help of Pi Times `○`):

```      1+*○0J1
0
```
Works in: Dyalog APL

## Properties

Exponential is a special case of Power with the default left argument of e (`*1`).

```      ((*1)∘* ≡ *) 0 1 ¯1 0J1
1
```
Works in: Dyalog APL

Exponential and natural log `⍟` are inverses of each other, except where the natural log is undefined.

```      (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1
1
(⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined
1
```
Works in: Dyalog APL