how come the calculator gives a solution for, per example, 2,4!

Someone (Probably CPhill) wrote a really good post on this a while ago.

It explained the concept to me quite nicely.  I can't find it - not here or on the wider net.

what a pity.  Chris, can you help?

There is a function called the gamma function that is related to factorials, but it is continuous.  When n is an integer then they are related by n! = gamma(n+1).

 

I guess the calculator here is trying to calculate gamma(3.4) as the continuous equivalent to 2.4!  However, it does it incorrectly, giving:

$${\mathtt{2.4}}{!} = {\mathtt{2.978\: \!344\: \!243\: \!007\: \!71}}$$

 

In fact gamma(3.4) = 2.9812064268...

 

(You can check this in WolframAlpha by typing gamma(3.4) in its input box)

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