The case q=1 (m=3,k=1) (Section 11.1)
Chebyshev polynomials
> | T:=proc(m) subs(cos(x)=x,expand(cos(m*x))): end: |
> | T(3); |
> | m:=3: k:=1: 2+2*cos(2*k*Pi/m); |
Introduce the series K. The second invariant is
> | I2:=normal(subs(C=CC,II=I1,Q(0,y)=K(y)/t^2/y/q,q=1,sqrt(C)^m*subs(x=xsubs,T(m)))); |
> | indets(I2); |
> | factor(series(normal(I2),y,1)); |
The invariant equation
> | eqinv:=subs(q=1,Q(0,y)=K(y)/t^2/y/q,q=1,beta=nu-1,I2-add(c[i]*(t*I1)^i,i=0..3)); |
> |
Determination of the series c_i
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