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Topic: Multinomial integration recurrence equations sought
Replies: 9   Last Post: Oct 4, 2011 2:45 PM

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 Albert D. Rich Posts: 311 From: Hawaii Island Registered: 5/30/09
Multinomial integration recurrence equations sought
Posted: Sep 11, 2011 1:51 PM

Six two-term 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, k-1) (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