√51+ϕ−1(−v+√1+v2)1/5−ϕ=e−2π√10/51+e−2π√101+e−4π√101+e−6π√101+⋱wherev=18−5√5
√51+ϕ−1(−v+√1+v2)1/5−ϕ=e−2π√15/51+e−2π√151+e−4π√151+e−6π√151+⋱wherev=147−55√54
where, as √5n increases, then v is an algebraic number of generally increasing high degree. I found this family using Mathematica and the second cfrac in Entry 3. This implies that the Rogers-Ramanujan continued fraction R(τ) R(i√n)=√51+ϕ−1R(i/√n)−ϕ
for some positive real n, though I have no proof of this assertion.
No comments:
Post a Comment