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#1 2012-10-22 02:21:33
- Mint
- Guest
Li(x)
What is li(x)?I know it is logarithmic integral function,but how do i find li(x),for instance,what will be li(5)?
#2 2012-10-22 03:08:45
- scientia
- Member
- Registered: 2009-11-13
- Posts: 224
Re: Li(x)
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#3 2012-10-22 03:40:17
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Li(x)
Hi Mint;
Welcome to the forum.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#4 2012-10-22 06:55:38
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Li(x)
You can use the series given at http://en.wikipedia.org/wiki/Logarithmi … esentation
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#5 2012-10-22 20:10:39
- Mint
- Guest
Re: Li(x)
That series is a little complex,isn't there a easier way?
#6 2012-10-22 20:20:45
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Li(x)
Depends on the arguments or how much accuracy you need. There are several ways for each.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2012-10-22 20:28:15
- Mint
- Guest
Re: Li(x)
Could you show me some
#8 2012-10-22 20:31:47
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Li(x)
Yes, but first I need that information from you.
1) Li(x), how big is x?
2)How many digits do you require because the answer is going to be in floating point.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2012-10-22 21:07:52
- Mint
- Guest
Re: Li(x)
I just want to know how to find li(x),but you could show an example of your own.
#10 2012-10-22 21:12:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Li(x)
Series are of different types. For small values of x we use Taylor series. For large values we use Asymptotic expansions and Series that are expanded around infinity.
1) You could try to evaluate the integral using Romberg or Gaussian integration.
2) You truncate the various series expansions producing smaller approximations.
3) You look up the values in tables.
I have used the second one to come up with an example:
When x>=500.
Read this:
http://numbers.computation.free.fr/Cons … rimes.html
now you will understand why there are only approximate answers.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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