A Linear Relation for Values of the Zeta Function at Even Positive Integers

The zeta function is like a milestone in analytic number theory. Considering Euler’s definition of the zeta function in this article, we will find some recursion at even integral points. We will also discuss the Dirichlet eta function, even Bernoulli numbers, and the gamma–zeta relation. Toward the end, we will define something known as the odd zeta function and find a recurrence for the same.