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Nested sums containing binomial coefficients occur in the computation ofmassive operator matrix elements. Their associated iterated integrals lead toalphabets including radicals, for which we determined a suitable basis. Wediscuss algorithms for converting between sum and integral representations,mainly relying on the Mellin transform. To aid the conversion we worked outdedicated rewrite rules, based on which also some general patterns emerging inthe process can be obtained.

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams