On Tue, May 6, 2008 at 9:04 AM, Henry Baker <hbaker1@pipeline.com> wrote:
I find it interesting that there are elegant formulae involving pi seem to come with additional coefficient baggage: e.g., pi/2, pi/4, 4pi, pi^2/6.
On the other hand, Euler's constant e seems to shine brightly from just one point. Are there any interesting formulae where e shows up with additional baggage?
Continued fractions whose terms involve arithmetic series are e + baggage. The easiest example is e-1 = [\overbar{1,1,2k}] Another example from Gosper's continued fraction entries in HAKMEM is [6; \overbar{3+6k}] = (4e^{2/3}-2) / (e^{2/3}-1) More formulae are here: http://www.numbertheory.org/php/davison.html -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com