
Multinomial integration recurrence equations sought
Posted:
Sep 11, 2011 1:51 PM


Six twoterm recurrence equations for integrands of the form
x^m (a+b x^n)^p
and six for integrands of the form
x^m (A+B x^n) (a+b x^n+c x^(2 n))^p
are available for viewing at http://www.apmaths.uwo.ca/RuleBasedMathematics/MultinomialRecurrenceEquations.pdf
Currently I am incorporating rules derived from these binomial and trinomial recurrences into version 4 of Rubi. However, I have a hunch there are six analogous quadrinomial recurrences for integrands of the form
x^m (A+B x^n+C x^(2 n)) (a+b x^n+c x^(2 n)+d x^(3 n))^p
Of course, the ultimate goal would be to discover multinomial recurrences for integrands of the form
x^m sum(Ai x^(i n), i, 0, k1) (sum(ai x^(i n), i, 0, k))^p
valid for any positive integer k. If anybody out there would like to contribute quadrinomial recurrences, or even better multinomial ones, Rubi would very much appreciate it.
Albert

