What does it mean for two curves parametrised about 0 (say the graph of two functions of real variable) to 'differ only by transcendentally small terms'? How does this relates to their Taylor expansion at 0?
2026-02-23 09:26:01.1771838761
Transcendental terms
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After some research in the direction of asymptotic series expansions, I think the meaning of transcendentally small is that it vanishes faster than any polynomial order. For example, for a power series expansion of the curve's equation, transcendentally small terms could be terms that vanish faster than any monomial involved in the power series representing it. Hence the two curves will have the same power series expansion, without being the same curve, since the 'transcendentally small terms' elude the description via power series, being described by the null power series themselves.