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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Derivatives of Whittaker functions $ W\sb{\kappa ,\,1/2}$ and $ M\sb{\kappa ,\,1/2}$ with respect to order $ \kappa $


Author: Bernard J. Laurenzi
Journal: Math. Comp. 27 (1973), 129-132
MSC: Primary 33A30; Secondary 81.33
MathSciNet review: 0364694
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Abstract: The Whittaker function derivatives $ {[\partial {W_{\kappa ,1/2}}/\partial \kappa ]_{\kappa = n}}$ and $ {[\partial {M_{\kappa ,1/2}}/\partial \kappa ]_{\kappa = n}}$ which arise in calculations involving the hydrogen atom's generalized Green's functions are computed.


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  • [1] H. Buchholtz, The Confluent Hypergeometric Function, Springer-Verlag, Berlin, 1969.
  • [2] L. Hostler, "Runge-Lenz vector and the Coulomb Green's function," J. Mathematical Phys., v. 8, 1967, p. 642.
  • [3] C. Jordan, Calculus of Finite Differences, Chelsea, New York, 1950, p. 543.
  • [4] Bernard J. Laurenzi, Green’s functions in atomic and molecular calculations, Chem. Phys. Lett. 1 (1967), 641–642. MR 0260328 (41 #4956)
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  • [7] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Fourth edition prepared by Ju. V. Geronimus and M. Ju. Ceĭtlin. Translated from the Russian by Scripta Technica, Inc. Translation edited by Alan Jeffrey, Academic Press, New York-London, 1965. MR 0197789 (33 #5952)
  • [8] Reference [1], p. 81.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0364694-3
PII: S 0025-5718(1973)0364694-3
Article copyright: © Copyright 1973 American Mathematical Society