Hey /sci/, has there been any kind of investigation into sums of the form [math]\sum_{k=0}^{\infty}D^k(f(x))[/math]

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Anonymous Fri Mar 10 18:34:57 2017 No.8737500 [Reply] [Original]

Hey /sci/, has there been any kind of investigation into sums of the form [math]\sum_{k=0}^{\infty}D^k(f(x))[/math]

>>	Anonymous Fri Mar 10 18:37:37 2017 No.8737507 They always converge to -1/12

Anonymous Fri Mar 10 18:56:37 2017 No.8737558

Here are a few things I suspect to be true. Could anyone prove them?

If that sum is positive it does not have to keep increasing. It could become negative.
If that sum is positive for sufficiently large intervals of x then f(x) is guaranteed to have a portion in that interval where it's increasing.

>>	Anonymous Sat Mar 11 11:23:53 2017 No.8739063 >>8737558 Look up Taylor series.

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/sci/ - Science & Math