Single-scale diagrams and multiple binomial sums

The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.Comment: 10 pp LaTeX, misprints in app. A and minor misprints in the text correcte

Two-loop self-energy master integrals on shell

Analytic results for the complete set of two-loop self-energy master integrals on shell with one mass are calculated.Comment: 14 pages, LaTeX, one eps-figure; in v5. misprints in the Eq.(2) and Table II correcte

Recursion relations for two-loop self-energy diagrams on-shell

A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2 package is used for the calculation of special types of diagrams. A method of calculation of higher order \epsilon-expansion of master integrals is demonstrated.Comment: Talk given by J.Fleischer at 6th International Workshop on Software Engineering, Artificial Intelligence, Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation (AIHENP 99), Heraklion, Crete, Greece, 12-16 April, 1999; 8 pages, LaTeX, 3 eps-figure