(this file is from Steve Finch, as sent by Joe Keane).

-----------------------------------------------------
I made some computations of Madelung's constant for various dimensions.
Here's a table of numerical values of M_n:

 n         M_n
--  ------------------
 1  1.3862943611198906
 2  1.6155426267128247
 3  1.7475645946331822
 4  1.8393990840450471
 5  1.9093378156187686
 6  1.9655570390090783
 7  2.0124059897979861
 8  2.0524668272692712
 9  2.0873943126737422
10  2.1183105013848236
11  2.1460101032438314
12  2.1710758356718034
13  2.1939472266380350
14  2.2149636885584330
15  2.2343925837496984
16  2.2524481350395574
17  2.2693045376544797
18  2.2851052778150323
19  2.2999698996586159
20  2.3139990132683816
21  2.3272780638661765
22  2.3398802115769973
23  2.3518685615728866
24  2.3632979123580459
25  2.3742161415965895
26  2.3846653158039725
27  2.3946825872032674
28  2.4043009247757267
29  2.4135497148671064
30  2.4224552582333393
31  2.4310411841736969
32  2.4393287977613929
33  2.4473373726952129
34  2.4550843996494696
35  2.4625857979725924
36  2.4698560970187535
37  2.4769085921775213
38  2.4837554797097914
39  2.4904079737422768
40  2.4968764081715069
41  2.5031703257469439
42  2.5092985562152292
43  2.5152692850936902
44  2.5210901143856934
45  2.5267681163413112
46  2.5323098811948176
47  2.5377215596684742
48  2.5430089009142076
49  2.5481772864665689
50  2.5532317606982057
51  2.5581770582000790
52  2.5630176284504981
53  2.5677576580878485
54  2.5724010910601329
55  2.5769516468888873
56  2.5814128372546652
57  2.5857879810852572
58  2.5900802183054573
59  2.5942925223879218
60  2.5984277118280198
61  2.6024884606511582
62  2.6064773080485455
63  2.6103966672264565
64  2.6142488335445563

[No word yet on the nature of Joe Keane's numerical methods.  I am
 under the impression that the alternating series themselves converge
 too slowly to be useful.  Also am unable to to find such a table
 anywhere else (but very likely I've overlooked it).

                                                S. Finch]

*****************************************************************************

Date: Fri, 10 Jan 1997 07:34:53 -0800 (PST)
From: Joe Keane
To: Steven Finch
Subject: Re: madelung

I found an expansion in terms of elliptic functions.  It's rather nasty,
and complicated to work out, but in the end it works well numerically.
I'm sure that someone has figured this out before, if we could find it.
I keep meaning to check up on references you give, since they sound
pretty interesting, but I don't get to the library very often...

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This page was modified January 10, 1997
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