Further Sums Found Through Fourier Series - Comments

Svein · Sep 28, 2017

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Further Sums Found Through Fourier Series

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kith · Oct 1, 2017

Quick Latex pointer: if you write "\left(" and "\right)" instead of "(" and ")" you get parentheses which self-adjust their height.

The Electrician · Oct 15, 2017

Mathematica gave this:

Four series identities in Mathematica output: sum from n=0 to infinity of 1/(1+n^2) equals (1 + pi Coth[pi])/2; sum from n=1 to infinity of (-1)^n/(1+n^2) equals (-1 + pi Csch[pi])/2; sum from n=0 to infinity of (-1)^n/(1+n^2) equals (1 + pi Csch[pi])/2; sum from n=1 to infinity of (-1)^n/(n-1/2)^3 equals -pi^3/4.

Svein · Oct 15, 2017

The Electrician said:

Mathematica gave this:

Then Mathematica and I agree. Fine!

For me this is part of the road I am currently going. As long as I am getting correct answers along the way, I am happy.

The Electrician · Oct 15, 2017

Svein said:

Then Mathematica and I agree. Fine!

For me this is part of the road I am currently going. As long as I am getting correct answers along the way, I am happy.

Did you notice that Mathematica disagrees on the sign of the last one?

Svein · Oct 16, 2017

The Electrician said:

Did you notice that Mathematica disagrees on the sign of the last one?

No, saw it just now. Mathematica is correct, the correct exponent for (-1) should be (n-1), not n.

Further Sums Found Through Fourier Series - Comments

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