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.
%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
}