A method is presented for an asymptotic expansion of the hydrogenic radial dipole integral for discrete-discrete transitions from initial state n'l' to final state nl. The advantage of this simple method is that it allows all the necessary algebraic manipulations to be done by the computer programming package REDUCE-2. Expansion coefficients up to the coefficient of the l/n17 term are obtained for all initial states with n' < or = 10. However, only the coefficients which are not calculated by Klarsfeld are tabulated in this paper.

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Abstract.The exact solution of a particular nonlinear partial differential equation is obtained in terms of solution « of a related linear partial differential equation. It is noted that solution may be found subject to initial conditions if certain initial conditions can be determined for solution u. Two examples are solved explicitly.R. T. Herbst [1] has pointed out that the ordinary nonlinear differential equation (1) / + p(x)y' + kq(x)y = (1 -Oy'y-1 + ßq(x)y1-ĥ as the solutionprovided that u satisfies the ordinary linear differential equation (3) u" + p(x)u + q(x)u = 0.