# Singular Euler-Maclaurin expansion

@article{Buchheit2020SingularEE, title={Singular Euler-Maclaurin expansion}, author={Andreas A. Buchheit and Torsten Kessler}, journal={ArXiv}, year={2020}, volume={abs/2003.12422} }

We generalise the Euler-Maclaurin expansion and make it applicable to the product of a differentiable function and an asymptotically smooth singularity. The difference between sum and integral is written as a differential operator acting on the non-singular factor only plus a remainder integral. The singularity can be included in generalised Bernoulli polynomials which form the coefficients of the differential operator and determine the integrand of the remainder integral. As the singularity is…

## One Citation

Singular Euler-Maclaurin expansion on multidimensional lattices

- MathematicsArXiv
- 2021

The singular Euler–Maclaurin (SEM) expansion is constructed, an extension of the previous work in one dimension, which remains applicable and useful even if the summand function includes a singular function factor.

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