An atlas of functions
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Introduction of small parameters to the real physical problems very often is a delicate and non-trivial problem and may be produced in the various ways. Here we analyze non-linear dynamical equation x + γx + ω2x + εxn = 0 for n → ∞.We propose new formula in the following form x = x0n√1+εnx1/x0, and this approach is compared with the usual one. We also obtained asymptotic solutions for Eq. (1) for γ = ω2 = 0, n → ∞ γ = 0, n → ∞. We show that cases ω2=0, n → ∞ and γ n → ∞ may be reduced to the previous ones.