Re: GenerateConditions->False gives fine result!
- To: mathgroup at smc.vnet.net
- Subject: [mg73876] Re: GenerateConditions->False gives fine result!
- From: Bhuvanesh <lalu_bhatt at yahoo.com>
- Date: Fri, 2 Mar 2007 06:39:36 -0500 (EST)
This is because the integral does in fact diverge in the Riemann sense. Taking the simpler example with {t->3, x->2}:
In[1]:= integrand = q/(E^(2*I*q)*Sqrt[q^2 + 9]);
In[2]:= Limit[integrand, q->Infinity]
Out[2]= (1 + I) Interval[{-1, 1}]
GenerateConditions->False, in addition to checking convergence and looking for singularities, also does Hadamard-type integrals. Here's another example:
In[1]:= Integrate[1/(x^(1 + I/2)*(1 + x)), {x, 0, 1}]
1
Integrate::idiv: Integral of ---------------- does not converge on {0, 1}.
1 + I/2
x (1 + x)
1
Out[1]= Integrate[----------------, {x, 0, 1}]
1 + I/2
x (1 + x)
In[2]:= Integrate[1/(x^(1 + I/2)*(1 + x)), {x, 0, 1}, GenerateConditions->False] //InputForm
Out[2]//InputForm= (-PolyGamma[0, -I/4] + PolyGamma[0, 1/2 - I/4])/2
Bhuvanesh,
Wolfram Research.