Re: Integrate modified in version 6?
- To: mathgroup at smc.vnet.net
- Subject: [mg78118] Re: Integrate modified in version 6?
- From: m.r at inbox.ru
- Date: Sat, 23 Jun 2007 07:10:45 -0400 (EDT)
- References: <f5asi1$9t6$1@smc.vnet.net>
On Jun 20, 4:38 am, dimitris <dimmec... at yahoo.com> wrote:
>
> Integrate[z ArcSin[z]/(1+z)^2, {z, 0, 1}]
> -Infinity
>
This is performance-dependent. On my machine:
In[1]:= Integrate[z*(ArcSin[z]/(1 + z)^2), {z, 0, 1}]
Out[1]= -Infinity
In[2]:= Dynamic[Pause[.5], UpdateInterval -> 1]
In[3]:= ClearSystemCache[]
ii = Integrate[z*(ArcSin[z]/(1 + z)^2), {z, 0, 1}]
Out[4]= 1/2 (MeijerG[{{-(1/2), 0}, {1}}, {{0, 0, 1/2}, {}}, 1] -
MeijerG[{{-(1/2), 0}, {1, 1}}, {{0, 0, 1/2, 1/2}, {}}, 1]/Sqrt[Pi])
The MeijerG expression is correct, the issue is that the simplifier
goes astray:
In[5]:= Cases[ii, _MeijerG, -1] // FunctionExpand
Out[5]= {-Infinity, MeijerG[{{-(1/2), 0}, {1, 1}}, {{0, 0, 1/2, 1/2},
{}}, 1]}
As a workaround, you can evaluate the MeijerG[]s as limits:
In[6]:= ii /. HoldPattern@ MeijerG[s__, 1] :>
Limit[FunctionExpand@ MeijerG[s, z], z -> 1] // Simplify
Out[6]= -1 - 2 Catalan + Pi (1/4 + Log[2])
Maxim Rytin
m.r at inbox.ru