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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