The summer package contains a number of FORM procedures and tables for the manipulation of harmonic sums. It is used also by the harmpol package. The library can be used for many classes of finite indefinite sums. It contains also extensive tables for relations between multiple zeta values, which are also called Euler-Zagier sums (harmonic sums in infinity).
The package is based on the paper:
J.A.M. Vermaseren: "Harmonic Sums, Mellin transforms and Integrals", Int. J. Mod. Phys. vol. 14 (1999) 2037.
Its files are:
| summer.h.gz | The library file with the FORM code. Please gunzip this file and put it in a location that is covered by your FORMPATH environment variable. |
| summerex.tar.gz | Some FORM programs that use summer.h. These are simple examples and a number of programs that derive all known relations between multiple zeta values up to weight 10. You may need the extra tables for weight 7-9. |
| table7.prc.gz | The weight 7 tables for multiple zeta values. Please gunzip this file and put it in a location that is covered by your FORMPATH environment variable. |
| table8.prc.gz | The weight 8 tables for multiple zeta values. Please gunzip this file and put it in a location that is covered by your FORMPATH environment variable. |
| table9.prc.gz | The weight 9 tables for multiple zeta values. Please gunzip this file and put it in a location that is covered by your FORMPATH environment variable. |
| summer.ps | The postscript version of the paper. |
| summer.pdf | The pdf version of the paper. |
The summer.h file contains tables for relations between the multiple zeta values up to weight 6. The others can be picked up when needed. This is to avoid the summer.h file to become too large. The tables for weight 10 are about 100 Mbytes and hence we didn't put them here. They can only be obtained and/or used on computers with a 64-bits architecture. Some of the runs in which they can be obtained have been used as benchmarks in the paper about tform.