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12:28 AM
Timing[ListPlot[Table[{x, Sum[(-1)^k Nest[x^# &, 1, k], {k, 1, 1000}]}, {x, 0.066,1.44, 0.01}]]]
@Vepir this is a line of code you had written in mathematica to make a plot of $\sum_{k=1}^{\infty} (-1)^k(^kx)$
how can we edit this to make a plot of $\sum_{k=1}^{\infty} (-1)^k(^{2k}x)$?
 
 
7 hours later…
7:11 AM
@Mathphile Change k to 2k?

Timing[ListPlot[Table[{x, Sum[(-1)^k Nest[x^# &, 1, 2k], {k, 1, 1000}]}, {x, 0.066,1.44, 0.01}]]]
Nest[x^# &, 1, k] is tetration (Nesting exponentiation k times) -> Nest[x^# &, 1, 2k]
 
7:48 AM
oh yes!! it is so obvious
i feel stupid now
thank you @Vepir
 
 
12 hours later…
8:04 PM
$$\sin x=\int_0^xe^{x^2-t^2}\,dt-\sum\limits_{n=0}^\infty\frac{(-1)^n(2^nn!-1)}{(2n+1)!}x^{2n+1}$$
through IBP
 
 
3 hours later…
10:58 PM
@Mathphile What does the plot look like?
 

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