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