Exponential
Revision as of 14:30, 14 July 2020 by Adám Brudzewsky (talk  contribs) (Text replacement  "http://help.dyalog.com" to "https://help.dyalog.com")
 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