Ratio of two Bessel function values

[Richard Guy]

I recently asked, on one of these networks,
about the number whose continued fraction
is  {1,2,3,4,...} and someone was kind
enough to provide an explicit answer, which
I've stupidly deleted.  Can it be repeated?

Incidentally, is there a more general
result, that a continued fraction whose
partial quotients form an arithmetic
progression (or a set of APs) can be
expressed in terms of Bessel functions?

There are a few examples which are
rational functions of  e.     R.