How to look up the value of a convergent sum

Asked Feb 13 '23 at 16:26

Active Feb 13 '23 at 16:26

Viewed 45 times

I would like to know if the value of the following double summation has been calculated:

$$\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2 + n^2}.$$

Any suggestions on how to look up such things in general? Is there a go-to dictionary for these sort of things?

Thanks

asked Feb 13 '23 at 16:26

Tom

1

How to prove $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2+n^2}=+\infty$ – Brevan Ellefsen Feb 13 '23 at 16:32
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Typing the sum into WolframAlpha can give a good indication in many cases. – Greg Martin Feb 13 '23 at 16:33
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Look them up via approachzero. All the common sums will be on this site already. – Brevan Ellefsen Feb 13 '23 at 16:33
oh... it doesn't converge... silly me! – Tom Feb 13 '23 at 16:49

0 Answers0