A documented set of FORM programs for the evaluation of sums over combinations of harmonic series, denominators and factorials. The techniques are also used in a program for Mellin transforms of functions occurring in Feynman diagram calculations. There are also programs for the calculation of harmonic series at infinity (related to Euler/Zagier sums). The whole is documented with the paper, a manual and lots of commentary in the programs. The paper can be retreived from the archive at Los Alamos . Its number is hep-ph/9806280. Of course it is also here: article .

The programs need version3 of FORM to run. This version is scheduled for the end of 1998.

This directory is still under construction, and hence it is not complete. Please check occasionally for progress.

Files

manual: The manual

a1.frm: The first example

a2.frm: The second example

nndecl.h: Declarations

basis.prc: Conversion to natural basis

sumnmii.prc: Triangle sum

tables.prc: Tables of values at infinity

table1.prc: table for weight 1

table2.prc: table for weight 2

table3.prc: table for weight 3

table4.prc: table for weight 4

table5.prc: table for weight 5

table6.prc: table for weight 6

table7.prc: table for weight 7

mel1.frm: Example of Mellin transform

mel2.frm: Difficult Mellin transform

mel3.frm: Example of integral

mel4.frm: Example of difficult integral

mel5.frm: Same difficult integral, other algorithm

meltran.h: Include file for Mellin program

bf2.frm: Value at infinity, weight 2

bf3.frm: Value at infinity, weight 3

bf4.frm: Value at infinity, weight 4

bf5.frm: Value at infinity, weight 5

bf6.frm: Value at infinity, weight 6

bf7.frm: Value at infinity, weight 7

bfn.h: Include file for bf programs

subesses.prc: S values for fixed argument

e.c: Evaluation of results from mel3,mel4,mel5.frm

ev.c: Program to obtain some constants

num.c: Numerical check of results by Monte Carlo integration