# [Maxima] Fourier transforms of some common function

Richard Hennessy rich.hennessy at verizon.net
Wed Jun 17 16:44:50 CDT 2009

```Hi all,

I have made a small chage to noninteractive.mac so it calls a function specified by the user instead of using 'if'.  Now it is
possible to do the following problems and get what I hope are the right answers.  I cannot verify the answers are correct since I
get an error trying to do the inverse Fourier transform which I have already reported to the bug list.  Hopefully this will be fixed
in the next version.

(%i1) (fun_to_call:pw1,ratprint:false);
(out1) false
(out2) C:/Maxima-5.18.1/share/maxima/5.18.1/share/contrib/noninteractive/noninteractive.mac
(%i3) integrate(1/(x^2+1)*exp(-2*%pi*%i*x*t),x,minf,inf);
(out3) %pi*%e^(-2*%pi*abs(t))
(%i4) integrate(1/(x^4+1)*exp(-2*%pi*%i*x*t),x,minf,inf);
(out4) (%e^(-sqrt(2)*%pi*abs(t))*(sqrt(2)*%pi*sin(sqrt(2)*%pi*abs(t))+sqrt(2)*%pi*cos(sqrt(2)*%pi*abs(t))))/2
(%i5) integrate(1/(x^6+1)*exp(-2*%pi*%i*t*x),x,minf,inf);
(out5)
(%e^(-2*%pi*abs(t))*(3*%pi*%e^(%pi*abs(t))*sin(sqrt(3)*%pi*abs(t))+sqrt(3)*%pi*%e^(%pi*abs(t))*cos(sqrt(3)*%pi*abs(t))+sqrt(3)*%pi))/(3*sqrt(3))
(%i6) integrate(1/(x^4+x^2+1)*exp(-2*%pi*%i*x*t),x,minf,inf);
(out6) (%e^(-sqrt(3)*%pi*abs(t))*(sqrt(3)*%pi*sin(%pi*abs(t))+%pi*cos(%pi*abs(t))))/sqrt(3)
(%i7) integrate(1/(x^6+x^4+x^2+1)*exp(-2*%pi*%i*x*t),x,minf,inf);
(out7)
(sqrt(2)*%e^((-sqrt(2)-2)*%pi*abs(t))*(2*%pi*%e^(2*%pi*abs(t))*sin(sqrt(2)*%pi*abs(t))+sqrt(2)*%pi*%e^(sqrt(2)*%pi*abs(t))))/4
(%i8) integrate(%pi*%e^(-2*%pi*abs(t))*exp(2*%pi*%i*x*t),t,minf,inf);
Maxima encountered a Lisp error:
Unhandled kernel in tvar-lim
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.

(%i9) pwdefint(%pi*%e^(-2*%pi*abs(t))*exp(2*%pi*%i*x*t),t,minf,inf);
Maxima encountered a Lisp error:
Unhandled kernel in tvar-lim
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.

Rich

```