Generating Function for Rotation Matrix Elements S. O ¨ . AKDEMIR, 1 E. O ¨ ZTEKIN 2 1 Department of Physics, Faculty of Education, Sinop University, Sinop, Turkey 2 Department of Physics, Faculty of Science and Arts, Ondokuz Mayis University, Samsun, Turkey Received 7 October 2010; accepted 29 November 2010 Published online 8 March 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/qua.23024 ABSTRACT: The rotation matrix elements are expressed in terms of the Jacobi, Hypergeometric, and Legendre polynomials in the literature. In this study, the generating function is presented for rotation matrix elements by using properties of Jacobi polynomials. In addition, some special values and Rodrigues’ formula of rotation matrix elements are obtained by using the generating function. V C 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112: 367–372, 2012 Key words: rotation matrix elements; generating function; Rodrigues’ formula 1. Introduction T he concepts of angular momentum and rota- tional invariance have come to occupy a more and more important position in the analy- sis of physical theories of nuclear and atomic structure. One reason for this is found in those improvements in experimental techniques, whereby, it has become possible to measure angular distribution in nuclear reactions or alter- natively angular correlations of successively emitted radiation. The theory of angular momen- tum, in its modern form, can be very advanta- geously applied to solution of problems associ- ated with the electric and magnetic multiple moments. It is well known that angular momentum oper- ators are proportional to the infinitesimal rota- tions. Under a finite rotation of the frame of refer- ence an eigenvector of J 2 is transformed a state vector with the same j. The term of rotation will be interpreted as a rotation of the frame of refer- ence about the origin, the physical system being supposed fixed. Each point of three-dimensional space is, thus, given new coordinates, which are functions of the old coordinates and of the param- eters, which describe the rotation, namely Euler angles, which we shall call a, b, and c. We shall now relate the operators D(abc) asso- ciated with finite rotations of the frame of refer- ence to the operators of infinitesimal rotations. It is convenient to write the matrix elements of D(abc) in a more compact form D j m 0 ; m abc ð Þ¼ e  im 0 a jm 0 h j e  i b J y jm j i e  im c (1) Correspondence to: S. O ¨ . Akdemir; e-mail: sozcan@sinop.edu.tr International Journal of Quantum Chemistry, Vol 112, 367–372 (2012) V C 2011 Wiley Periodicals, Inc.