Some sort of transform to find the log of a series

[onanox]

I am trying to write a computer program that involves finding 2 very large numbers (several thousand digits) and dividing them to get a reasonable sized number.
the first number is a value of the gamma function, which can be defined as a product and thus easy to reduce with logs (find the sum of the log of each term).

hoewever the second number is a value of the incomplete gamma function, which AKAIK can only be defined as a sum. clearly, if I just log each term and sum them, id get the log of the product and thus, no dice. However, if I could find some transform for each term, that when summed would equal the log of the total sum, my problems would be solved.

Has anyone heard of anything like this?

 

[Mute]

This recently revived thread might help: https://www.physicsforums.com/showthread.php?t=101181

It discusses turning infinite sums into infinite products and vice versa.

 

[onanox]

the problem is that each term in the series is too large to compute with standard data types, and that thread defines a product based on a sum and thus will not work.

 

[Stephen Tashi]

A time honored way of answering a internet post about "How do I do this..." is to reply "You don't want to do that...". It isn't necessarily relevant to your post, but it might be wise to explain exactly what you are trying to do - in case there is some special trick that applies to the situation but not in general or in case there is a way to avoid the problem altogether.

You should also clarify whether if you are determined not to use a specialized arbitrary precision numerical library like GNU Bignum in your program. Are you trying to get this to work in ordinary double precision floating point arithmetic?

 

[onanox]

good point, I guess I was a bit vague.
I am trying to calculate the incomplete-gamma function specifically for large arguments (around 50,000).
I am using as3 to program it, and there isn't any flexibility on the language.

 

[Stephen Tashi]

I am trying to calculate the incomplete-gamma function specifically for large arguments (around 50,000).
I am using as3 to program it,

Well, at least the question isn't "How do I model nuclear reactions using my Excel spreadsheet?".

I did a Google search on the words: large values incomplete gamma function
I found this PDF which reports how it was coded in FORTRAN:

http://www.google.com/url?sa=t&sour...p_msDQ&usg=AFQjCNGNyI6Ky4KtzwHvc-IgHDANnCXPmA

(See section D.)

One problem you are going to have is checking your routine. There is always the possibiity of typos in you coding or even in the printed matter you based the code upon.
It's handy to be able to compare your answers to output from a standard numerical library.