The Basel problem

The work’s primary goal was to create a new and original solution to the Basel problem, the statement of which is to find the sum of reciprocals of squares of all positive integers. The prestented approach  mainly aims for being as free of an application of very strong mathematical theorems which would be hard to prove as possible. In addition the approach can be further easily generalized so it would provide the general formula for the sum of reciprocals of any even integer powers. The solution itself primarily relies on a manipulation with the gamma function and the psi function, later derived from the gamma function. As the secondary goal the work also presents an original proof of the reflection formula for the gamma function, which is generaly very hard to prove.

Contestants

Alexandr Jankov