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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
DOI: https://doi.org/10.1090/S0025-5718-1973-0364694-3
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.
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  • [5] B. J. Laurenzi, "Green's functions in atomic and molecular calculations," J. Chem. Phys., v. 52, 1970, p. 3049.
  • [6] Y. L. Luke, The Special Functions and Their Approximations. Vol. 1, Math. in Sci. and Engineering, vol. 53, Academic Press, New York, 1969, p. 115. MR 39 #3039.
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  • [8] Reference [1], p. 81.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0364694-3
Article copyright: © Copyright 1973 American Mathematical Society

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