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Using energy eigenfunctions obtained by semi-empirical analysis of the Lu-Fano plot of energy level positions and employing the Coulomb approximation of Bates and Damgaard, we calculate absolute line strengths for transitions between the neon two-channel Rydberg series 2p5(2P3/2,1/2)ns J = 1 and 2p5 (2P3/2,1/2)n′ p J = 0 for n, n' = 3,4. Each Rydberg series is analyzed separately to obtain a set of five parameters which completely define the energy eigenfunctions for all values of n and n'. Interactions between the ns J = 1 and the nd J = 1 Rydberg series have been ignored. The one-channel neon p and s series are also discussed and line strengths for transition between them presented. Our line strengths for 3s → 3p and 4s → 4p transitions are in excellent agreement with the experimental and theoretical work of others. Our results for 3s → 4p and 4s → 3p transitions are not in agreement with previous work and differ substantially with intermediate coupling theory. For our application to low-lying energy levels in neon we have had to correct the formulas of Lu and Fano by inclusion of the energy-dependent factors of Seaton and by assuming a linear dependence on energy of intrinsic scattering phase shifts. We present all formulas necessary for computing absolute line strengths for transitions between multi-channel Rydberg series.