The complete sums




Here we have all Euler or alternating sums of a given weight. The only things missingare the divergent sums, but those can easily be expressed in terms of the finite ones and powers of the basic divergent sum Sinf.

The basis elements are characterized by that they are Lyndon words over the negative odd integers.

The .log files are the results of the runs of the hexall.frm program.

hexall-2.log.bz2 Weight 2, (533)
hexall-3.log.bz2 Weight 3, (645)
hexall-4.log.bz2 Weight 4, (912)
hexall-5.log.bz2 Weight 5, (1974)
hexall-6.log.bz2 Weight 6, (6710)
hexall-7.log.bz2 Weight 7, (34546)
hexall-8.log.bz2 Weight 8, (193837)
hexall-9.log.bz2 Weight 9, (1180719)
hexall-10.log.bz2 Weight 10, (7700572)
hexall-11.log.bz2 Weight 11, (51151694)
hexall-12.log.bz2 Weight 12, (342213202)

The .prc files contain the complete tables of the finite elements. Note that the tables for the weights 1-6 are in the file hexall.h.

alt7.prc.bz2 Weight 7, (33099)
alt8.prc.bz2 Weight 8, (191117)
alt9.prc.bz2 Weight 9, (1170728)
alt10.prc.bz2 Weight 10, (7685893)
alt11.prc.bz2 Weight 11, (51022344)
alt12.prc.bz2 Weight 12, (341222257)

The corresponding .sav files are

alt7.sav.bz2 Weight 7, (28418)
alt8.sav.bz2 Weight 8, (178472)
alt9.sav.bz2 Weight 9, (1131295)
alt10.sav.bz2 Weight 10, (7720533)
alt11.sav.bz2 Weight 11, (52005415)
alt12.sav.bz2 Weight 12, (343461352)

and the .tbl files

alt7.tbl Weight 7, (374600)
alt8.tbl Weight 8, (1321701)
alt9.tbl Weight 9, (5069807)
alt10.tbl Weight 10, (21910628)
alt11.tbl Weight 11, (109666540)
alt12.tbl Weight 12, (609089016)

And the programs:

hexall.frm The program, (7898)
hexall.h The library for hexall.frm, (147349)
form.set The form setups as used on a 32 Gbyte system, (311)
altlow.h The tables for weight 1-6, (52208)