is this a new bug? Mathematicaa 5.0...
- To: mathgroup at smc.vnet.net
- Subject: [mg43145] is this a new bug? Mathematicaa 5.0...
- From: w1rw1ck at hotmail.com (steven)
- Date: Thu, 14 Aug 2003 05:08:01 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
( I simplified the Mathematica copy/paste to make somewhat readable.. )
In =
Assuming[b > 0 && [Omega] > 0 && b [NotEqual] [Omega] ,
Integrate[
(Sin[b t]/(b t)) [ExponentialE]^([ImaginaryI][Omega]t),
{t, (-[Infinity]), [Infinity]}]])
Out = 0 ( think this should be a "rectangle" function.. )
In =
Assuming[ b > 0 && [Omega] > 0 &&
b [NotEqual] [Omega] && k > 0,
Integrate[
( Sin[b t]/(b t)) [ExponentialE]^([ImaginaryI] [Omega]
t), {t, (-k), k}]]
Out = ( long wait... then.. )
-((1/(2 b))(([ImaginaryI] ((CosIntegral[
k ((b - [Omega]))] -
CosIntegral[k (((-b) + [Omega]))] - Log[b - [Omega]] +
Log[(-b) + [Omega]] +
2 [ImaginaryI] SinIntegral[k ((b - [Omega]))] +
2 [ImaginaryI] SinIntegral[k ((b + [Omega]))])))))
Now:
In = Limit[the above.., k goes to infinity]
Out = ( long wait.. )
<< same as input.. >>
when plotting, as k gets bigger, the graph looks more and more like
the rectangle we all know it should be..
and boy, it sure takes a long time to get the initial integrate to
even come to zero
thanks
Steven