A Symbolic Summation Approach to Find Optimal Nested Sum Representations

Abstract

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.

To appear in Clay Mathematics Proceedings

References in corpus (5)

• Harmonic Sums and Mellin Transforms up to two-loop Order
• A Refined Difference Field Theory for Symbolic Summation
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• Parameterized Telescoping Proves Algebraic Independence of Sums
• Difference Equations in Massive Higher Order Calculations

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• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
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• Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations
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• 3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering