Derivatives of Whittaker functions $W_{\kappa , 1/2}$ and $M_{\kappa , 1/2}$ with respect to order $\kappa$
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- by Bernard J. Laurenzi PDF
- Math. Comp. 27 (1973), 129-132 Request permission
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.References
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H. Buchholtz, The Confluent Hypergeometric Function, Springer-Verlag, Berlin, 1969.
L. Hostler, "Runge-Lenz vector and the Coulomb Green’s function," J. Mathematical Phys., v. 8, 1967, p. 642.
C. Jordan, Calculus of Finite Differences, Chelsea, New York, 1950, p. 543.
- Bernard J. Laurenzi, Green’s functions in atomic and molecular calculations, Chem. Phys. Lett. 1 (1967), 641–642. MR 260328, DOI 10.1016/0009-2614(68)80104-6 B. J. Laurenzi, "Green’s functions in atomic and molecular calculations," J. Chem. Phys., v. 52, 1970, p. 3049. 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.
- I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York-London, 1965. Fourth edition prepared by Ju. V. Geronimus and M. Ju. Ceĭtlin; Translated from the Russian by Scripta Technica, Inc; Translation edited by Alan Jeffrey. MR 0197789 Reference [1], p. 81.
Additional Information
- © Copyright 1973 American Mathematical Society
- 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