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This paper demonstrates that the degree-n truncation of the formal exponential function preserves the power sum constraints for any arbitrary sequence of complex numbers. The main theorem establishes that the roots of the truncated polynomial exactly match the prescribed power sums for the first n terms, providing an O(n²) algorithm for computation. The results are applied to the polylogarithm family, linking the findings to values of the Riemann zeta function.

Author

ste amr

Language

EN