## Another proof of Euler’s formula for $$\zeta(2k)$$.(English)Zbl 1223.40001

For Euler’s famous evaluation in question, there is an abundance of proofs. The authors give another one which they “believe” to be “simpler than those cited” in their long list of references. Here, Euler’s formula results from comparing two series representations of $$\int\tan xy\text{ d}x$$, $$|x|\leq \pi/2$$, $$|y|<1$$, by unspecified reference to “Fubini’s theorem”.
Reviewer’s remark: At the first representation, the index $$k$$ instead of $$n$$ would be appropriate for later identification. – In the last equation line, the factor has to change sides.

### MSC:

 40A25 Approximation to limiting values (summation of series, etc.)
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### References:

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