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Re: GenerateConditions->False gives fine result!


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.


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