Euler Maclaurin formula for functions with singularities

92 Views Asked by At

Is there a version of the Euler Maclaurin formula for treating functions having singularities ?

for example $$ \sum_{k=0}^{99} \sum_{x=0}^{n} \frac{1}{\frac{k}{100} + \frac{\sqrt{x^2 + d})}{100} - 1} $$

Note: I know there's a partial sum formula for this but it includes the Polygamma of negative values which I'm trying to avoid.