- from A. Salat, Plasma Physics, Vol. 17, p. 589-607, (1975).
- common form of the integrals

- transformation of variables, new form

- sum of 288 terms up to the 9-th degree in ,
one term of the 9-th degree in gives after
substitutions 19 683 terms, in one part of one collision integral
is 259 584 terms (one term is a product appearing in a sum)
- integration over derived from

- integration over ; rotation and
transformation into spherical coordinates

- integration over , products
, elimination of

- integration over

- integration over

- final result contains only elementary functions and the error function
- algebraic program in REDUCE was unable to calculate all the collision
integrals and so had to be rewritten into a more efficient symbolic
program
- speed up of the symbolic program compared to the algebraic program
depends on the size of a collision integral
Size small medium large Speed up 3x 7x ?

Richard Liska