Exponential
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 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