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some sort of transform to find the log of a series

  • 27-06-2011 10:06am
    #1
    bcvdbgfs
    Closed Accounts Posts: 8 ✭


    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?


Comments

  • #2
    RoundTower
    Registered Users, Registered Users 2 Posts: 5,083 ✭✭✭RoundTower


    bcvdbgfs wrote: »
    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.

    I'm not sure what you mean here. It sounds like you want something which it is easy to show does not exist. But there are other ways to approach the problem.

    What kind of precision do you need, and how fast does the calculation have to run? That's much more important than knowing the numbers will have "thousands of digits". In principle you should be able to get whatever precision you need in a reasonable amount of time using GMP.


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