Performing this technique on the regularized Riemann zeta function is done to show that the sum of the natural numbers converges to -1/12.
This technique is used on algebraic approximants to build solutions to power flow equations in the HELM method. This process can be performed starting from a given point and proceeding along rays, a configuration known as the Mittag-Leffler star. It cannot be performed on power series which contain gaps between their nonzero terms according to the Hadamard-Ostrowski theorem; it also cannot be performed if all points on the circle of convergence for a function are singular. Doing this process along a curve with overlapping disks is possible via the monodromy theorem. Performing this technique on the regularized Riemann zeta function is done to show that the sum of the natural numbers converges to -1/12. The gamma function can be defined over the entire complex plane by using, for 10 points, what technique that extends the domain of a complex-differentiable function?
This technique is used on algebraic approximants to build solutions to power flow equations in the HELM method.
analytic continuation [prompt on extension of a domain or continuation]