# [Maxima] laplace transform

Raymond Toy toy.raymond at gmail.com
Thu Feb 26 19:22:32 CST 2009

```Andrej Vodopivec wrote:
>>> 3/ Since I assumed s>0, I expected the answer to be given in a real form,
>>> I mean without %i in it. How can we "simplify" this answer to atan(2/s) ?
>>> Is there a quite general way to do it ?
>>>
>> I don't know how to get anything simpler than
>> atan2(4*s/(s^2+4),(s^2-4)/(s^2+4))/2.  It seems to me that we could at
>> least have atan2(4*s,s^2-4)/2, but I don't know how to get maxima to do
>> that.  I also don't know why you think the answer is atan(2/s).  Is that
>> the answer in some table of transforms?
>>
>
> (%i1) assume(s>0);
> (%o1) [s>0]
> (%i2) u:specint(sin(2*t)/t*exp(-s*t),t);
> (%o2) (%i*log((s-2*%i)/(s+2*%i)))/2
> (%i3) rectform(u), logexpand=all;
> (%o3) atan(2/s)
>
>
Neat.  But log(x/y) is not always the same as log(x) - log(y).   And for
s = 1/2, I get different answers.  But I think they're the same for s >=
2.  Also, in general, isn't the Laplace parameter s a complex number?

Ray

```