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In control theory, overshoot refers to an output exceeding its final, steady-state value. [2] For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step
For a step input, the percentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the overshoot is just the maximum value of the step response minus one. The percentage overshoot (PO) is related to damping ratio (ζ) by:
In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function = =. Zeta functions include: Airy zeta function, related to the zeros of the Airy function; Arakawa–Kaneko zeta function; Arithmetic zeta function
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
These values may be expressed as ratios [2] or, equivalently, as percentages [3] with respect to a given reference value. In analog electronics and digital electronics, [citation needed] these percentages are commonly the 10% and 90% (or equivalently 0.1 and 0.9) of the output step height: [4] however, other values are commonly used. [5]
In number theory, the local zeta function Z(V, s) (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as (,) = (= ())where V is a non-singular n-dimensional projective algebraic variety over the field F q with q elements and N k is the number of points of V defined over the finite field extension F q k of F q.
In mathematics, the Riemann–von Mangoldt formula, named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros of the Riemann zeta function. The formula states that the number N ( T ) of zeros of the zeta function with imaginary part greater than 0 and less than or equal to T satisfies
The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.