>>> So where is the problem in calculating such expressions?
>>
>> I don't have a copy of Maxima.
>
> Included in any decent distribution... let's troll an OS war again (not!)
> That's not Mathematica's license fee.

I'd still have to learn Maxima, and I'd still have the problem that what 
I actually want is to write a program myself which computes the answers 
as part of its work. I don't really want an external dependency on a 
sophisticated math package.

>> The real problem is that I want to write computer software which
>> computes P-values for the results it obtains. The fact that all these
>> distributions are so numerically intractable to operate with makes that
>> a rather difficult task.
>
> If you want to play with big numbers by yourself, there is C libraries
> about that. They are often used in cryptography but can be used to
> perform computation on unlimited integers.
>
> Have a look at GNU MP for instance.

I don't really want to play with big numbers; I want to compute a 
P-value. It's just that the formula for the binomial distribution 
happens to involve large numbers as intermediate results. The other 
distributions have the problem that they all involve exotic functions 
which nobody can compute (most prominently the gamma function).

If there were a way to approximate these distributions reasonably well 
(especially in the tails), that would be preferable.

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