Towards a Parallel Summation Algorithm
CoRR(2024)
摘要
We propose a summation analog of the paradigm of parallel integration. Using
this paradigm, we make some first steps towards an indefinite summation
algorithm applicable to summands that rationally depend on the summation index
and a P-recursive sequence and its shifts. Under the assumption that the
corresponding difference field has no unnatural constants, we are able to
compute a bound on the normal part of the denominator of a potential closed
form. We can also handle the numerator. Our algorithm is incomplete so far as
we cannot predict the special part of the denominator. However, we do have some
structural results about special polynomials for the setting under
consideration.
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