%0 Journal Article %1 springerlink:10.1007/s10910-011-9914-4 %A Weniger, Ernst %D 2012 %I Springer Netherlands %J Journal of Mathematical Chemistry %K analysis basis chemistry function mathematics orthogonal quantum review series set %N 1 %P 17-81 %R 10.1007/s10910-011-9914-4 %T On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions %U http://dx.doi.org/10.1007/s10910-011-9914-4 %V 50 %X Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are expansions in terms of Slater-type functions with a common scaling parameter and integral principal quantum numbers. This was accomplished by expressing the complete and orthonormal Laguerre-type functions as finite linear combinations of Slater-type functions and by rearranging the order of the nested summations. Essentially, this corresponds to the transformation of a Laguerre expansion, which in general only converges in the mean, to a power series, which converges pointwise. Such a transformation is not necessarily legitimate, and this contribution discusses in detail the difference between truncated expansions and the infinite series that result in the absence of truncation.

@article{springerlink:10.1007/s10910-011-9914-4, abstract = {Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are expansions in terms of Slater-type functions with a common scaling parameter and integral principal quantum numbers. This was accomplished by expressing the complete and orthonormal Laguerre-type functions as finite linear combinations of Slater-type functions and by rearranging the order of the nested summations. Essentially, this corresponds to the transformation of a Laguerre expansion, which in general only converges in the mean, to a power series, which converges pointwise. Such a transformation is not necessarily legitimate, and this contribution discusses in detail the difference between truncated expansions and the infinite series that result in the absence of truncation.}, added-at = {2012-01-20T04:28:56.000+0100}, affiliation = {Institut für Physikalische und Theoretische Chemie, Universität Regensburg, 93040 Regensburg, Germany}, author = {Weniger, Ernst}, biburl = {https://www.bibsonomy.org/bibtex/22e968d33255171f0f5edaf07fb468d93/drmatusek}, doi = {10.1007/s10910-011-9914-4}, interhash = {e67448d41b911687c301cf85974253e8}, intrahash = {2e968d33255171f0f5edaf07fb468d93}, issn = {0259-9791}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {analysis basis chemistry function mathematics orthogonal quantum review series set}, month = {January}, note = {10.1007/s10910-011-9914-4}, number = 1, pages = {17-81}, publisher = {Springer Netherlands}, timestamp = {2013-03-23T16:32:24.000+0100}, title = {On the mathematical nature of Guseinov’s rearranged one-range addition theorems for Slater-type functions}, url = {http://dx.doi.org/10.1007/s10910-011-9914-4}, volume = 50, year = 2012 }