Re: [math-fun] Are these two numbers equal?

I tried this (for free) on Wolfram Alpha, and it says the same thing. It gives the following expressions for the two integrals: -1/18 i (π^2 - 36 Li_2((-1)^(1/3))) 1/18 i (π^2 - 36 Li_2((-1)^(1/3))) which clearly sum to zero. (It says Li_n is the polylogarithm function.) Tom Dan Asimov writes:

Thanks! (That HAD to be true since no two real numbers can be as close as these were.)

—Dan

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According to maple they are symbolically equal. I did not dig into it to try to see why.

On Mon, Aug 20, 2018 at 5:19 PM Dan Asimov <dasimov@earthlink.net> wrote:

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Let f(x) = ln(2-2*cos(x))

Then are these two numbers equal?

A = -Integral from 0 to π/3 of f(t) dt

B = Integral from π/3 to π of f(t) dt

I can't tell. But they're extremely close.

—Dan