|
%I #33 Sep 27 2020 14:03:28
%S 1,3,3,7,2,3,5,7,0,1,4,3,0,6,8,9,4,0,8,9,0,1,1,6,2,1,4,3,1,9,3,7,1,0,
%T 6,1,2,5,3,9,5,0,2,1,3,8,4,6,0,5,1,2,4,1,8,8,7,6,3,1,2,7,8,1,9,1,4,3,
%U 5,0,5,3,1,3,6,1,2,0,4,9,8,8,4,1,8,8,8,1,3,2,3,4,3,8,7,9,4,0,1,5,6,1,0,3,8
%N Decimal expansion of imaginary part of solution to z = log z.
%C Repeatedly take logs, starting from any number not equal to 0, 1, e, e^e, e^(e^e), etc. and you will converge to 0.31813150... + 1.33723570...*I.
%H Stanislav Sykora, <a href="/A059527/b059527.txt">Table of n, a(n) for n = 1..2000</a>
%H Stanislav Sykora, <a href="https://doi.org/10.3247/SL6Math16.002">Fixed points of the mappings exp(z) and -exp(z) in C</a>, 2016.
%H Wolfram Research, <a href="https://reference.wolfram.com/language/ref/FixedPoint.html">FixedPoint</a>
%e z = 0.31813150520476413531265425158766451720351761387139986692237... + 1.33723570143068940890116214319371061253950213846051241887631... *i.
%t RealDigits[ Im[ N[ FixedPoint[ Log, 1 + I, 910], 105]]] [[1]]
%t RealDigits[ N[ Im[ ProductLog[-1]], 105]][[1]] (* _Jean-François Alcover_, Feb 01 2012 *)
%o (PARI) z=I;for(k=1,16000,z=log(z));imag(z) \\ Using realprecision \p 2010. - _Stanislav Sykora_, Jun 07 2015
%o (PARI) z=I; for(k=1, 10, z-=(z-log(z))/(1-1/z)); imag(z) \\ _Jeremy Tan_, Sep 23 2017
%Y Real part is A059526.
%Y Cf. A030178.
%K cons,nonn,nice
%O 1,2
%A _Fabian Rothelius_, Jan 21 2001
%E More terms from _Vladeta Jovovic_, Feb 26 2001
%E Edited and extended by _Robert G. Wilson v_, Aug 22 2002
|
