In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician...

Riemann integral but based on Darboux sums, is equivalent to the Riemann integral. Loosely speaking, the Riemann integral is the limit of the Riemann...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers...

is called (R,k) (or Riemann) summable to s if lim h → 0 ∑ n a n ( sin ⁡ n h n h ) k = s . {\displaystyle \lim _{h\rightarrow 0}\sum _{n}a_{n}\left({\frac...

thought of the area under a curve as an infinite sum of rectangles of infinitesimal width. Bernhard Riemann later gave a rigorous definition of integrals...

In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes....

in the above Riemann sum yields I = lim Δ t → 0 ∑ i = 1 n f ( r ( t i ) ) | r ′ ( t i ) | Δ t {\displaystyle I=\lim _{\Delta t\to 0}\sum _{i=1}^{n}f(\mathbf...

mathematics, the Riemann series theorem, also called the Riemann rearrangement theorem, named after 19th-century German mathematician Bernhard Riemann, says that...

oscillating functions the Riemann sum can be arbitrarily far from the Riemann integral. The formulae below involve finite sums; for infinite summations...