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 Zeta sine (Posted on 2018-10-28)
What is the maximum value of the expression below?

sin x / 13 + sin 2x / 23 + sin 3x / 33 + ...

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 re(2): Solution (spoiler) | Comment 3 of 6 |
(In reply to re: Solution (spoiler) by Charlie)

When Wolfram Alpha is asked to evaluate

sum  sin(k*x) / k^3,k=1 to infinity

it produces

1/2 i (Li_3(e^(-i x)) - Li_3(e^(i x)))

When it's asked to

plot   1/2 i (Li_3(e^(-i x)) - Li_3(e^(i x))), x=0 to 400

the graph seems to vary only between -1 and 1.

It seems to reach a local maximum of 1 at about 4003.7, for example, when plotting between x=4002 and 4005.

 Posted by Charlie on 2018-10-31 11:56:13
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