I don't know about naming here, but if you are going to attempt searching on numeric results, you might want something more precise than ^^. to obtain a decimal representation.
For example: 0j16 ": 851897554247r254074700880 3.3529412857573449 I hope this helps, -- Raul On Mon, Dec 26, 2022 at 6:50 AM Martin Kreuzer <[email protected]> wrote: > > Hi all -- > > - 1 ----- > > Inspired by lately reading up on the Kempner series I tried this > modification (depletion) of the harmonic series: > > fib >: i.13 > 1 1 2 3 5 8 13 21 34 55 89 144 233 > % fib >: i.13 > 1 1 1r2 1r3 1r5 1r8 1r13 1r21 1r34 1r55 1r89 1r144 1r233 > +/ % fib >: i.13 > 851897554247r254074700880 > ^^. +/ % fib >: i.13 > 3.35294128575735 > NB. ... > > ^^. +/ % fib >: i.50 > 3.3598856661144394 > ^^. +/ % fib >: i.60 > 3.3598856662422096 > ^^. +/ % fib >: i.70 > 3.3598856662429739 > ^^. +/ % fib >: i.80 > 3.3598856662433558 > > and have been wondering about convergence/divergence. > > - 2 ----- > > In parallel I did this > > fib i.13 > 0 1 1 2 3 5 8 13 21 34 55 89 144 > ecf fib i.13 > 2882971364492r4895735924493 > ^^. ecf fib i.13 > 0.588874 > > NB. (fib) producing Fibonacci numbers > NB. (ecf) evaluating a Continued Fraction > > and have wondered whether this constant had a name (since the Fib > numbers themselves are fairly famous), and in what other contexts it > might pop up. > > NB. The Wolfram|Alpha equivalent would have been > NB. FromContinuedFraction[Fibonacci[Range[0,13]]] > > ----- > > Could you shed some light on these (while keeeping in mind that I'm > not a mathematician). > > Thanks (and with season's greetings) > > -M > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
