A Symbolic Summation Approach to Find Optimal Nested Sum Representations

Computer Science – Symbolic Computation

Scientific paper

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To appear in Clay Mathematics Proceedings

Scientific paper

We consider the following problem: Given a nested sum expression, find a sum
representation such that the nested depth is minimal. We obtain a symbolic
summation framework that solves this problem for sums defined, e.g., over
hypergeometric, $q$-hypergeometric or mixed hypergeometric expressions.
Recently, our methods have found applications in quantum field theory.

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