Classic Fourier Series

[salvomic]

FourCoeff Version "all in one":
Input something like function or expression (with variable) and k:
g(t) -> "g, k", g(x) -> "g, x, k", "t^2, k", "x^2, x, k"... where k = (0), 1, 2, ...
It calculate the Fourier coefficient (trigonometric and exponential).
I hope the formulas be good, please control...

The output is sure "wild", it must be presented more clean, sorry...
My idea was to print the letter and the interval, but doing so the row is sure too long...
Any help appreciated.

Code:


ChooseInterval()
BEGIN
  LOCAL choice;
  CHOOSE(choice,"Interval", "from 0 to 2pi", "from -pi to pi");
  RETURN choice;
END;

#cas
fourcoeff(args):=

BEGIN
local argv,argc,f,k;
local ak, bk, a0,ck;
argv:=[args];
argc:=size(argv);
f := argv(1);
k := argv(argc);
IF argc=3 THEN f:=zip('unapply', f, argv(2)); END;

IF EXPR(" FourCoeff.ChooseInterval()")=1 THEN 
a0:=(int(f(t),t,0,2*PI))/(2*PI);
ak:=(int(f(t)*cos(k*t),t,0,2*PI))/PI;
bk:=(int(f(t)*sin(k*t),t,0,2*PI))/PI;
ck:=( int(f(t)*e^(-i*k*t),t0,pi))/pi;
return "0..2pi a0", a0, "a,b", {ak, bk}, "c", ck; ELSE
a0:=(int(f(t),t,0,pi))/(2*pi);
ak:=(int(f(t)*cos(k*t),t,-pi,pi))/pi;
bk:=(int(f(t)*sin(k*t),t,-pi,pi))/pi;
ck:=( int(f(t)*e^(-i*k*t),t,-pi,pi))/(2*pi);
return "-pi..pi a0", a0, "a,b", {ak, bk}, "c",ck;
END;

END;
#end

Everyone can adapt it at his/hers needs

Salvo M.