Classic Fourier Series

[salvomic]

there was an error in a formula...
Output like vector, a little better than the first one...
(Please tell me the true syntax of Return command: how to do to have two lines, ho to avoid "" and have "labels", without using ' ' (that evaluate expression)...

Code:


ChooseInterval()
BEGIN
LOCAL choice;
CHOOSE(choice,"Interval","From 0 to 2π","From −π to π");
RETURN choice;
END;

#cas
fourcoeff(args):=
// Coefficienti di Fourier formula normale,  by Salvo Micciché v 1.0
// input funzione fourcoeff(func, k) o espressione fourcoeff(expr, var, k)
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),t,0,2*pi))/(2*pi);
RETURN {"[0,2π] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck}; ELSE
a0:=(int(f(t),t,-pi,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 {"[-π,π] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck};
END;

END;
#end