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Expansions of Coulomb wave functions in terms of Bessel functions

✍ Scribed by A.S. Meligy; E.M. El Gazzy

Publisher
Elsevier Science
Year
1962
Weight
178 KB
Volume
36
Category
Article
ISSN
0029-5582

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dn u + k cn u A . (dn u + k cn u)~'", A . ( d n u -k c n u d n u -k c n u the expansions for A (u) and A (u) being suitable for ~-dnu+(:nu i I > -; d n u h c c n u 3c B.(-. dn u ~-+ k cn -) u d n u -k c n u the expansions for H [ x (u)] and B [ z (u)] being suitable for -~ B . -\_ \_ ~ , -( dn uk cn

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An expansion is derived for the regular (power series) part of the Coulomb function, \(G_{0}(\eta, \rho)\), in terms of Whittaker functions, which are closely related to the regular Coulomb functions \(F_{1}(n, \rho)\). The expansion coefficients are given as a sum of three terms; each of the terms