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Analytical and numerical treatment of auxiliary function \({B_{m^\prime m}^j \left(\beta\right)}\) for finite rotation matrix elements

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Abstract

In this study, a new method evaluate the auxiliary function \({B_{m^\prime m}^j \left( { \beta }\right)}\) which the function appears in the matrix elements \({d_{m^\prime ,m}^j \left( \beta \right)}\) are formulated. Also, the generating functions, Rodrigues’ formula, and orthogonality relationships for the \({B_{m^\prime m}^j \left( { \beta }\right)}\) function are presented. To analyze their formal mathematical structure, \({B_{m^\prime m}^j \left( { \beta } \right)}\) functions are expressed in terms of the Jacobi, Gegenbauer, Legendre, and Chebyshev polynomials. \({B_{m^\prime m}^j \left( { \beta }\right)}\) 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).

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Authors and Affiliations

  1. Department of Physics, Faculty of Science and Arts, University of Ondokuz Mayıs, 55139, Kurupelit, Samsun, Turkey

    Emin Öztekin

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  1. Emin Öztekin
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Correspondence to Emin Öztekin.

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Öztekin, E. Analytical and numerical treatment of auxiliary function \({B_{m^\prime m}^j \left(\beta\right)}\) for finite rotation matrix elements. J Math Chem 46, 448–458 (2009). https://doi.org/10.1007/s10910-008-9470-8

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  • DOI: https://doi.org/10.1007/s10910-008-9470-8

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