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** Up:** Families of Continued Fractions
** Previous:** Levesque and Rhin's Families

##

Unverified Families

The following is a list of functions which appear to be families
of continued fractions, because a computer program written by the
author in the summer of 1999 showed that for small values for the
variables in *M*, the period of
grew linearly. These
results would be highly unlikely if *M* where in fact not a family
of continued fractions.
Let
*F* = 4*a* + 1, let *j* = 1 when *a* = 1, and let *j* = 2 when
*a* > 1.

Where
*E* = 4*a* - 1,

Also, where *p* = 0 for *a*= 1 and *p* = 1 for *a*> 1,

Now let,
,
with *d* > 2; then,

Letting
where *d* > 2, one finds,

Let
with *d* > 2; then,

Where
with *d* > 2, one has

Looking at *G* again,

Similarly with *N*,

Some more families involving *G*:

The sort of patterns above can also be seen in *N*:

Though the following continued fractions have only one variable,
their growth rate is significant (for two of them), so it should
be useful to mention them.

** Next:** The Fundamental Correspondence
** Up:** Families of Continued Fractions
** Previous:** Levesque and Rhin's Families
*mcenter*

*2000-01-06*