Am Sonntag, den 22.08.2010, 12:46 +0200 schrieb Sergio Callegari:
> Hi,
>
> I define the following
>
> f(psi,beta):=%e^(beta*(asin((2*psi)/%pi)-atan2(1,beta)+%pi/2))*cos(asin((2*psi)/%pi)-atan2(1,beta))
>
> and I have issues in getting the taylor series around zero, while
> considering beta a constant.
>
> for instance
>
> taylor(f(psi,beta),psi,0,0);
>
> returns
>
> (%o69)/T/
> (sqrt(beta^2+1)*(beta+%i)^(%i*beta)*%e^((%pi*beta)/2)*beta)/((beta^2+1)^((%i*beta)/2)*beta^2+(beta^2+1)^((%i*beta)/2))+...
>
> where the imaginary unit is somehow weird.
>
> Any clue?
A workaround is not to use the names "psi" and "beta". Both names
represent Maxima functions. The symbols might have special properties.
I get the following
(%i45) f(psi,beta):=%e^(beta*(asin((2*psi)/%pi)-atan2(1,beta)+%
pi/2))*cos(asin((2*psi)/%pi)-atan2(1,beta));
(%o45) f(psi,beta):=%e^(beta*(asin(2*psi/%pi)-atan2(1,beta)+%pi/2))
*cos(asin(2*psi/%pi)-atan2(1,beta))
Here I use the variables x and y and not psi and beta. I have not
checked the result:
(%i46) taylor(f(x,y),psi,0,0);
(%o46) +cos(asin(2*x/%pi)-atan2(1,y))*%e^((asin(2*x/%pi)-atan2(1,y)+%
pi/2)*y)
Nevertheless it is interesting to look at what point the imaginary unit
is introduced in the result.
Dieter Kaiser