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I just skimmed through, but I didn’t see the method I expected to find: Use the Taylor series for f(x) = e^x around f(0) to compute e = f(1). Should be pretty e
by bjornsing 5y ago
I just skimmed through, but I didn’t see the method I expected to find: Use the Taylor series for f(x) = e^x around f(0) to compute e = f(1). Should be pretty efficient and straightforward, right?
- clangcmp 5y agoThey did. They called it Newton's series
- not2b 5y agoYes, the Taylor series converges very quickly, but for some reason the author insists on only using the problem that originally introduced Bernoulli and Euler to the number e.
- raiph 5y agoThe author not only included Taylor's (Newton's) but the superior Brother's.
- phkahler 5y ago>> but I didn’t see the method I expected to find: Use the Taylor series for f(x) = e^x around f(0) to compute e = f(1) Is that the one where e = 1 + 1/1! + 1/2! + 1/3! + ... ? Steve Wozniak used that method to compute several thousand digits of e on an Apple II back in the day. I think Byte ran an article on it. Super easy because each term is just the previous term divided by N.
- thaumasiotes 5y agoYes, that's the Taylor series.
- raiph 5y agoIt's included (he calls it Newton's), and he follows it with the even better Brother's.