In this study, a new method evaluate the auxiliary function B(m'm)(j) (beta) which the function appears in the matrix elements d(m',m)(j) (beta) are formulated. Also, the generating functions, Rodrigues' formula, and orthogonality relationships for the B(m'm)(j) (beta) function are presented. To analyze their formalmathematical structure, B(m'm)(j) (beta) functions are expressed in terms of the Jacobi, Gegenbauer, Legendre, and Chebyshev polynomials. B(m'm)(j) (beta) functions and their linear combinations are calculated numerically for large values of the indices j, m', m quantum numbers and beta angles by using generating function. Finally, evaluating numerical values for them are checked with obtained control expressions and results of Oztekin and Ozcan (J Math Chem 44: 28, 2008).