Re: integrate issue (5.2)
- To: mathgroup at smc.vnet.net
- Subject: [mg77136] Re: integrate issue (5.2)
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Mon, 4 Jun 2007 03:58:30 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <f3u3u4$2kr$1@smc.vnet.net>
dimitris wrote: > This is quite trivial so I am sure it has been pointed > out a long time ago. > In fact I believe that mathematica 6 does not > show this buggy behavior. > > Anyway... > > In[32]:= > $Version > > Out[32]= > "5.2 for Microsoft Windows (June 20, 2005)" > > In[40]:= > LaplaceTransform[Log[t], t, o] > Out[40]= > -((EulerGamma + Log[o])/o) > > which is correct. > > However > > In[42]:= > Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}, GenerateConditions -> > True] > > returns divergence message which is not in general truth. Try for > example > > In[44]:= > Integrate[(Log[t]*Exp[(-#1)*t] & ) /@ {1, 4, 10}, {t, 0, Infinity}] > Out[44]= > {-EulerGamma, -(EulerGamma/4) - Log[2]/2, (1/10)*(-EulerGamma - > Log[10])} > > Being more specifying, > > In[47]:= > Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}, Assumptions -> s > 0] > Out[47]= > -((EulerGamma + Log[s])/s) > > The integral converges for Re[s]>0, but Mathematica (5.2) fails to > detect this. Hi Dimitris, Although this does not solve your problem, you are right in assuming that version 6.0 correctly handles the different cases. In[1]:= Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}, GenerateConditions -> True] Out[1]= If[Re[s] > 0, -((EulerGamma + Log[s])/s), Integrate[Log[t]/E^(s*t), {t, 0, Infinity}, Assumptions -> Re[s] <= 0]] In[2]:= Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}] Out[2]= If[Re[s] > 0, -((EulerGamma + Log[s])/s), Integrate[Log[t]/E^(s*t), {t, 0, Infinity}, Assumptions -> Re[s] <= 0]] In[3]:= Integrate[(Log[t]*Exp[(-#1)*t] & ) /@ {1, 4, 10}, {t, 0, Infinity}] Out[3]= {-EulerGamma, -(EulerGamma/4) - Log[2]/2, (1/10)*(-EulerGamma - Log[10])} In[4]:= Integrate[Log[t]*Exp[(-s)*t], {t, 0, Infinity}, Assumptions -> s > 0] Out[4]= -((EulerGamma + Log[s])/s) Regards, Jean-Marc