Orchid XP v8 wrote:
> Kevin Wampler wrote:
> 
>> Did you read the Wikipedia page on closed form expressions?  It's not 
>> very long and all of these points are addressed there.
> 
> ...OK, just read it. Doesn't seem to address very much.

I was thinking of:



trigonometric functions and inverse trigonometric functions)."

and

"For purposes of numeric computations, being in closed form is not in 
general necessary, as many limits and integrals can be efficiently 
computed."

Which seem to exactly cover both of the points you recently mentioned, 
but perhaps I misunderstood what points you were making.


> Also, I've often wondered how the **** you compute something like the 
> Gamma function or the Bessel-J function. I mean, have you *seen* the 
> definition?!

Yes.  If you take a look at the Wikipedia article for the gamma function 
you'll see that it includes a couple of nice representations in terms of 
infinite products.  The Bessel functions seem a bit more involved, but 
it has representations in terms of a sum over terms involving the gamma 
function, a hypergeometric series, and a recursive relation to a 
continued fraction -- so there seem to be many ways to go about 
computing it (I didn't look up what the standard approach in practice was).

I know that you say that you have trouble digesting the Wikipedia 
articles on these in full (entirely understandable, they are very dense 
and not always well written) but you still can answer these questions by 
spending a minute or two just skimming over them without trying to 
understand everything.

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