In the course of searching for continued fraction identities, Raayoni (2021) and Elimelech et al. (2023) noticed that while
the numerator and denominator
of continued fraction convergents 
in general grow factorially (
for some positive integer 
), the reduced numerator and
denominator 
and 
for 
grew at most exponentially (
).
This phenomenon has been termed "factorial reduction" and, while it is extremely rare in general (Elimelech et al. 2023), it holds for all identities originally found by the Ramanujan Machine (Raayoni et al. 2021, Elimelech et al. 2023). It is illustrated above for the Apéry constant continued fraction
![6/(zeta(3))=5+K_(n=1)^infty(-n^6)/(17[n^3+(n+1)^3]-12(2n+1)).](/images/equations/FactorialReduction/NumberedEquation1.svg) |
