Conversion from series to continued fraction

 .

 .

 .

So we can say that

  in special form

Recall that the following consecutive form

in 0114. Now there is no b₀ and a₂,a₄,a₆, . . . are all ones. We get

Thus

In the same way, we have

.

 .

 .

So we can say that

  in special form

where there is some pattern except the first two terms. Applying the same rule in 0114

and we get

Thus