This is behavior that could be expected when you evaluate _any_ infinite Taylor ... | Hacker News

Hacker Newsnew | past | comments | ask | show | jobs | submit

		zests on Sept 13, 2019 \| parent \| context \| favorite \| on: The exponential function is a miracle This is behavior that could be expected when you evaluate _any_ infinite Taylor series far enough away from where the series is centered. Denominators of a typical Taylor series are fixed and the numerators depend polynomially on x. The post is definitely an interesting observation. I would chalk the miracle up to Taylor series and analytic functions in general, however.

joppy on Sept 13, 2019 | [–]

I guess the miracle is that the series converges everywhere. For example, the Taylor series for log(1 + x) only converges for |x| < 1.

stkdump on Sept 13, 2019 | [–]

Exactly. Imagine how their mind would be blown when evaluating sin(1000pi), which is exactly 0 with the taylor series of sin(x) centered around x=0.

Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact