Evaluation of recurrence relationships and numerical solutions for finite rotation matrix elements by using auxiliary functions

Abstract

In this article, we derived several new recurrence relations of the rotation matrix elements by using Gauss' recurrence formulas for hypergeometric functions and auxiliary functions A(m',m)(j)(beta), and B-i,l(k)(beta). The aim of this contribution is to obtain general algorithm to compute the rotation matrix elements, paying attention to the use recurrence relationships of the auxiliary functions that allow the treatment of the functions with high angular momentum quantum numbers.