IBIS expresses a class of finite inverse binomial sums with harmonic sums as S-sums using new telescoping recursions, and ships as a FORM package.
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
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abstract
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
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IBIS: Inverse BInomial sum Solver
IBIS expresses a class of finite inverse binomial sums with harmonic sums as S-sums using new telescoping recursions, and ships as a FORM package.