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**Mint****Guest**

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)?

**scientia****Member**- Registered: 2009-11-13
- Posts: 224

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

You can use the series given at http://en.wikipedia.org/wiki/Logarithmi … esentation

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**Mint****Guest**

That series is a little complex,isn't there a easier way?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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**Mint****Guest**

Could you show me some

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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**Mint****Guest**

I just want to know how to find li(x),but you could show an example of your own.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,262

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.****No great discovery was ever made without a bold guess. **

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