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#1 2012-10-23 01:21:33

Mint
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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)?

scientia
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#3 2012-10-23 02:40:17

bobbym

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Re: Li(x)

Hi Mint;

Welcome to the forum.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#4 2012-10-23 05:55:38

anonimnystefy
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Re: Li(x)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2012-10-23 19:10:39

Mint
Guest

Re: Li(x)

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

#6 2012-10-23 19:20:45

bobbym

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2012-10-23 19:28:15

Mint
Guest

Re: Li(x)

Could you show me some

#8 2012-10-23 19:31:47

bobbym

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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#9 2012-10-23 20:07:52

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 2012-10-23 20:12:41

bobbym

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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.