Conversion from other form to continued fraction

Recall that

   in special form

as in 0301 in the conversion from binomial expansion to continued fraction.

So we set x=exp(2*x) in the formula at the beginning and we get the following

When x=exp(2x) and y=-1,

When x=exp(2x) and y=1,

    for

Since

when x=1/x in the formula at the beginning

When y=1