Regular form of continued fraction

A special notation of continued fraction

where b₀ can be missing.

Operations of continued fraction(consecutive applications)

(1)

Rule 1(down->reciprocals current up and next up)

Its consecutive form(as in 0110)

(2)

Rule 2(both->next down & next next up)

Its consecutive form

(3)

Yesterday’s rule (gamma-shaped expansion)

A variant

Its consecutive form