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

```

• Prev by Date: Re: Combination List
• Next by Date: Parallel Computing Toolkit 2.1 now available
• Previous by thread: Re: Re: Integrate modified in version 6?
• Next by thread: Re: Integrate modified in version 6?