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+--- Thread: the " average restart " of a number. (/showthread.php?tid=845)
the " average restart " of a number. - tommy1729 - 03/26/2014
Let z be a nonreal complex number.
z=z1
z2=exp(z1)
z3=exp(z2)
etc
Define f(x) as f = 1 if x is within the unit circle on the complex plane ( |x| < 1 ) and 0 otherwise.
Let ar_b(z) denote the " average restart " of z.
"ar_b" is defined by a limit of an integer n going to +oo.
ar_b(z) = lim_n [f(z1) + f(z2) + f(z3) + ... + f(zn)]/n^b = constant(z).
(b > 0)
What is known about this ??
regards
tommy1729