 Indeed, at large ξ the solution of in the first approximation by 1/ξ is

where "A" is constant; the multiplier formula_55 makes χ a small quantity so it can be substituted in by sh 2χ ≈ 2χ.From one obtains

After determining α and β from and and expanding "e"α and "e"β in series according to the above approximation, one obtains finally