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From: Frederick Williams on 1 Jul 2010 09:25
Han de Bruijn wrote:
>
> On Jul 1, 1:31 am, Gerry Myerson <ge...(a)maths.mq.edi.ai.i2u4email>
> wrote:
> > In article
> > <271b2a4b-1624-4f50-a1d8-2c48b39cf...(a)y4g2000yqy.googlegroups.com>,
> >
> > TCL <tl...(a)cox.net> wrote:
> > > The derivative of an arithmetic function f:Z^+ -> C is defined as
> >
> > > f'(n)=f(n)log n
> >
> > > Does anyone know who first defined this definition? Dirichlet?
> > > I can't find this info from Google.
> >
> > Pentti Haukkanen, of Tampere, has written on this (although I think
> > he uses f'(n) = - f(n) log n), maybe you should try to contact him.

>
> Any idea about the heuristics or where it's good for?

Without the minus sign? See my reply to David Ullrich. Apostol goes on
to prove the Selberg identity using it. I don't know if that was
Selberg's approach: a quick look at Hardy & Wright's historical notes
may settle it.

--
I can't go on, I'll go on.
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