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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: 222

Re: Li(x)

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#3 2012-10-22 03:40:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

Re: Li(x)

Hi Mint;

Welcome to the forum.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#4 2012-10-22 06:55:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Li(x)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,864

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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