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Riemann zeta function for nonnegative even integers. The Riemann zeta function for negative even integers is 0 (those are the trivial zeros of the Riemann zeta function). The Riemann zeta function for nonnegative even integers is given by (note that is the only rational number for nonnegative even integers) where are the Bernoulli numbers.
The arc length functional has as its domain the vector space of rectifiable curves (a subspace of), and outputs a real scalar. This is an example of a non-linear functional. The Riemann integral is a linear functional on the vector space of Riemann-integrable functions from to.