The case q=1 (m=3, k=1) (Section 10.1)
The 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); |
> | I2:=normal(subs(C=CC,II=I1,q=1,yinv=1/y,M(1,y)=M(y),normal(sqrt(C)^m*subs(x=xsubs,T(m))))): |
> | factor(series(normal(I2),y=1,1)); |
The invariant equation:
> | eqinv:=subs(M(1,y)=M(y),q=1,I2-add(c[i]*I1^i,i=0..3)): |
> |
> | indets(eqinv); |
> |
> |
Determination of the series c_i. One obtains an equation with a single catalytic variable y, and one additional unknown series K(1) (or M(1))
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