# Exponential: Difference between revisions

 `*`

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 <source lang=apl inline>*</syntaxhighlight> with the dyadic arithmetic function Power.

## Examples

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

<source lang=apl>

```     *1
```

2.718281828 </syntaxhighlight>

On APL implementations that support complex numbers, one can demonstrate Euler's identity (with the help of Pi Times <source lang=apl inline>○</syntaxhighlight>):

<source lang=apl>

```     1+*○0J1
```

0

</syntaxhighlight>

Works in: Dyalog APL

## Properties

Exponential is a special case of Power with the default left argument of e (<source lang=apl inline>*1</syntaxhighlight>).

<source lang=apl>

```     ((*1)∘* ≡ *) 0 1 ¯1 0J1
```

1

</syntaxhighlight>

Works in: Dyalog APL

Exponential and natural log <source lang=apl inline>⍟</syntaxhighlight> are inverses of each other, except where the natural log is undefined.

<source lang=apl>

```     (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1
```

1

```     (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined
```

1

</syntaxhighlight>

Works in: Dyalog APL