4 Oct
2005
4 Oct
'05
4:23 p.m.
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