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MathGroup Archive 2006

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Re: question about the inverse li function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65383] Re: question about the inverse li function
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Wed, 29 Mar 2006 06:34:25 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 3/28/06 at 4:05 AM, Arthur.Capet at student.ulg.ac.be (Capet Arthur)
wrote:

>the question...

>i've measured C(x), wich is equal to li(I(x)), where li denotes the
>logarithmic integral function. I would like to compute I(x)=
>li^(-1) (C(x))

>how can i compute the inverse of the logarithmic integral function
>? Is there a function Inverse[_function] ?

Yes, there is a function for computing inverses of functions, InverseFunction. But, function will only provide and inverse function where there is a defined inverse function. That is,

InverseFunction[Sin] gives

ArcSin

but

InverseFunction[LogIntegral] won't give you something useful.

One way to solve the problem would be to use FindRoot, i.e.

In[10]:=
FindRoot[LogIntegral[x] == -1, {x, 1.1}]

Out[10]=
{x -> 1.1882560662743253}

or if you wanted the other root

In[16]:=
FindRoot[LogIntegral[x] == -1, {x, 0.9}]

Out[16]=
{x -> 0.7674077436558667}
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