asymptotic expansion

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asymptotic expansion A series A0 + A1/z + A2/z2 + … + An/zn + …,

that may either converge for large values of |z| or diverge for all values of z, is called an asymptotic expansion of the function F(z), valid in a given range of values of arg z, if, for every fixed value of n, the expression zn(F(z) – A0A1/z – A2/z2 – … – An/zn)

tends to zero as |z| → ∞, while arg z remains in the given range.