Analytical and Numerical Treatment of Auxiliary Function Bm'mj(beta) for Finite Rotation Matrix Elements

Abstract

In this study, a new method evaluate the auxiliary function B <inf>m′m</inf>J which the function appears in the matrix elements d<inf>m′,m</inf>J(β) are formulated. Also, the generating functions, Rodrigues' formula, and orthogonality relationships for the B<inf>;m′m</inf>;;J;(β) function are presented. To analyze their formal mathematical structure, B<inf>;m′m</inf>; ;J;(β) functions are expressed in terms of the Jacobi, Gegenbauer, Legendre, and Chebyshev polynomials. B<inf>m′m</inf> J(β) functions and their linear combinations are calculated numerically for large values of the indices j, m′, m quantum numbers and β angles by using generating function. Finally, evaluating numerical values for them are checked with obtained control expressions and results of Öztekin and Özcan (J Math Chem 44:28, 2008). © 2008 Springer Science+Business Media, LLC.