[seqfan] Re: Chewing an old bone
davidwwilson at comcast.net
Fri Oct 14 02:35:37 CEST 2011
From a visual standpoint, your function would probably work just as
well, although it turns
out that |qlog(x)| is closer to |log(x)| than is your proposed function
for every nonzero x.
BTW, qlog is the inverse of f(x) = 10^x - 10^-x, which if you
contemplate for a bit, explains
why it hugs log so closely for large values.
On 10/13/2011 5:36 AM, Alois Heinz wrote:
> The idea is good.
> But why not
> signum(a(n)) * log(|a(n)|+1)
> which is compatible with log(|a(n)|+1) for nonnegative sequences?
> Am 13.10.2011 04:14, schrieb David Wilson:
>> My suggestion to improve this situation is as follows: For
>> large-valued sequences, instead of plotting
>> log(a(n)+1) or log(|a(n)|+1), plot
>> qlog(n) = arcsinh(a(n)/2)/(ln 10)
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