06/29/2011, 08:39 PM
Code:
base 1.63532449671527639934534
fixed point 1.63698995729105702725471 + 1.52462061222409266551551*I
...
pentation base 1.63532449671527639934534
pentation(-0.5) 0.540797083552851488750873
sexp fixed point -1.64087257571659334856123
sexp slope at fixed 4.80600575430175169638439
pentation period 4.00236960853189042690462*I
pentation singularity -1.64567803532871618956796 + 2.00118480426594521345231*I
pentation precision, via sexp(pent(-0.5))-pent(0.5)
-8.68755408487736716409823 E-22
complex sexp Taylor series centered at 3.0885322718067176544821807826411
sexp base, sexp(upfixed)=upfixed 1.6353244967152763993453446183062
init;loop iterations required 7
upfixed, parabolic fixed point 3.0885322718067176544821807826411
sexp'(upfixed) base B 1.0000000000000000000000000000000
sexp(upfixed)-upfixed error 9.7027744501722372002703206199650 E-33
? sexp(3.000)
%210 = 3.0022195105134555312059775955040
? pent(2.000)
%184 = 2.0088543076992014631570864956219
Let
The interesting things about this base are that several values shown above are close to
Furthermore, base
Code:
? exp(1/2)
%42 = 1.6487212707001281468486507878142
? sexp(1/2)
%43 = 1.6463542337511945809719240315921
? pent(1/2)
%44 = 1.6323247404360631184869762532583
? pent(-3)
%45 = -1.6363583542860289796292230421033
Are these all 'coincidencies' or is there some good reason for the minute differences between these values? Any reason for it seems rather obscure, it's like a puzzle, a mystery to figure out. That is why I call that number, the 'enigma constant'.
Perhaps one can use base