       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:= integrand = q/(E^(2*I*q)*Sqrt[q^2 + 9]);

In:= Limit[integrand, q->Infinity]

Out= (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:= 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= Integrate[----------------, {x, 0, 1}]
1 + I/2
x        (1 + x)

In:= Integrate[1/(x^(1 + I/2)*(1 + x)), {x, 0, 1}, GenerateConditions->False] //InputForm

Out//InputForm= (-PolyGamma[0, -I/4] + PolyGamma[0, 1/2 - I/4])/2

Bhuvanesh,
Wolfram Research.

```

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