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We present solidfmm, a highly optimised C++ library for the solid harmonicsas they are needed in fast multipole methods. The library provides efficient,vectorised implementations of the translation operations M2M, M2L, and L2L, andis available as free software. While asymptotically of complexity $O(P^3)$, forall practically relevant expansion orders, the translation operators display anempirical complexity of $O(P^2)$, outperforming the na\"ive implementation byorders of magnitude.

Solidfmm: A highly optimised library of operations on the solid harmonics for use in fast multipole methods