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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 Riemann Sum and the Definite Integral. We begin our introduction to the Riemann Sum by considering non-negative functions which are. continuous over an interval []a,b . To simplify the explanation and the calculations, the interval. []a,b will be divided into subintervals of equal width, and the sample points will correspond to. the right endpoints of the subintervals. A more general/rigorous treatment of the Riemann Sum. may be found in the calculus textbook used by Pure and Applied Science students.