[seqfan] Re: Simple formulas for Madelung constants?

Neil Sloane njasloane at gmail.com
Mon Feb 19 15:34:22 CET 2018


Jon,  The answer is certainly Yes.  However, you
have to be very careful when calculating these Madelung constants.  As you
will
see if you look at the literature (Finch page 76 is a good start) these
sums need to
be interpreted very carefully, since they have subsequences
which are divergent.

Yes, you can write down expressions like

Sum_{i, j, k not all 0} f(i,j,k)

where f(i,j,k) = (-1)^(i+j+k)/sqrt(i^2+j^2+k^2).

but then you need to say exactly what you mean.  We are working here with
potentially
divergent sums.  My advice would be not to blindly start running some
computer program.
Do some research first.



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sun, Feb 18, 2018 at 10:04 PM, <jonscho at hiwaay.net> wrote:

> The Formula section of A085469 gives a formula of the form
>
>      Sum_{i, j, k not all 0} f(i,j,k)
>
> (In this case, f(i,j,k) = (-1)^(i+j+k)/sqrt(i^2+j^2+k^2).)
>
> Is there a similar formula (differing only in its function f(i,j,k)) for
> A181152, A182565, A182566, or A182567?
>
> Thanks!
>
> -- Jon
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>


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