Re: bug in Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg74810] Re: bug in Integrate*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Fri, 6 Apr 2007 04:19:41 -0400 (EDT)*References*: <ev2b70$kh1$1@smc.vnet.net>

Aha! The key is the setting GenerateConditions->True. But even though I have encountered one a couple of integrals that the explicit setting GenerateConditions->True was necessary for getting desirable results, it still looks mysterious why it is needed to add this setting since the default options of Integrate contain it! Ooops... Options[Integrate] {Assumptions :> $Assumptions, GenerateConditions -> Automatic, PrincipalValue -> False} I have forgotten this! Consequently, the default setting is GenerateConditions -> Automatic and so for this integrals Integrate[...,GenerateConditions -> Automatic] (*default*) fail to detect the divergence. Information[GenerateConditions] "GenerateConditions is an option for Integrate that specifies whether explicit conditions on parameters should be generated in \ the results of definite integrals." Attributes[GenerateConditions] = {Protected} BUT Reading from the help-browser... "The default setting is GenerateConditions->Automatic, which is equivalent to a setting of True for one dimensional integrals". Now I get more confused! Can you give a little more insight? Thanks again! Dimitris =CF/=C7 Bhuvanesh =DD=E3=F1=E1=F8=E5: > Thanks for the report. This has already been fixed in the development ver= sion for quite a while. In this case, you can get the expected divergence u= sing GenerateConditions->True, which does more extensive checking: > > In[1]:= $Version > > Out[1]= 5.2 for Microsoft Windows (June 10, 2005) > > In[2]:= Integrate[x*BesselJ[0, x]*Cos[x], {x, 0, Infinity}, GenerateCon= ditions->True] > > Integrate::idiv: Integral of x BesselJ[0, x] Cos[x] does not converge on = {0, Infinity}. > > Out[2]= Integrate[x BesselJ[0, x] Cos[x], {x, 0, Infinity}, GenerateCon= ditions -> True] > > In[3]:= Integrate[x*BesselJ[0, x]*Sin[x], {x, 0, Infinity}, GenerateCon= ditions->True] > > Integrate::gener: Unable to check convergence. > > Integrate::idiv: Integral of x BesselJ[0, x] Sin[x] does not converge on = {0, Infinity}. > > Out[3]= Integrate[x BesselJ[0, x] Sin[x], {x, 0, Infinity}, GenerateCon= ditions -> True] > > Bhuvanesh, > Wolfram Research.