asymptotic expansion

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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/zA2/z2 − … − An/zn)

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

Subjects: Computing.

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