Analytical derivation of higher-order terms of Molière's series and accuracy of Molière's angular distribution of fast charged particles

Molière's series functions of higher orders describing angular distributions of charged particle under the multiple scattering process are solved by exactly evaluating Cauchy integral with poles within the contour of integration. The functions of Molière's series giving higher-order terms are evaluated accurately by Poisson series expansion, both for spatial and projected angular distributions. Molière's series for the integrated angular distributions are also derived. Accuracy of the Molière's series expansion of higher orders is examined by comparing the reconstructed angular distributions with those derived exactly through the numerical Hankel transforms