Ratio of two Bessel function values

[Richard Guy]

Many thanks!    R.

On Tue, 4 Oct 2005, Eric W. Weisstein wrote:

> On Tue, 4 Oct 2005, Richard Guy wrote:
>
>> 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.
>
> Yes; see 
> http://mathworld.wolfram.com/ContinuedFractionConstant.html
>
> Cheers,
> -Eric
>