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Hi Keckman, I just briefly looked at your code. From your definitions: You treat the partial polynomials as *numbers* (correct me if I err, but the extended data type is not suitable for polynomials but just for real numbers). Well, the factorial of 1000 e.g. would require about 8530 binary digits ... After all, you have to deal with polynomials using tuples / lists of their respective coefficients. Hope this is not too patronizing: But the Lagrange polynomials are a real pain; why not use the Newton polynomials (look for "divided differences"). But I'm afraid you won't get good approximations in this case just with say a 3rd degree polynomial.
It all started out some years ago when I read how the number e was introduced / defined. I thought to myself: Hey, why not explore the sequences
Let
such that . DefineLooking at the sequence of partial sums
:Now pick some positive real number r. Define
Then for all integers n such that
Define
So finally we get
From books written in Bourbaki-style! -- I am not on 'very friendly terms' with algebra; yet I like the book of B. L. Van der Waerden. Now take any oh so modern book -- say about group theory, with several pages of notation and what not ... horrible. I think Gauss said / wrote: "We need notions, not notations!" (btw, you can sing that on "another brick in the wall" :-)).
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