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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 typi
by zests 7y ago
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.
- stkdump 7y agoExactly. 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.
- joppy 7y agoI guess the miracle is that the series converges everywhere. For example, the Taylor series for log(1 + x) only converges for |x| < 1.