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Siegel derived it from the Riemann–Siegel integral formula, an expression for the zeta function involving contour integrals. It is often used to compute values of the Riemann–Siegel formula, sometimes in combination with the Odlyzko–Schönhage algorithm which speeds it up considerably.
In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function.
In mathematics, the Riemann–Siegel theta function is defined in terms of the gamma function as = ((+)) for real values of t.Here the argument is chosen in such a way that a continuous function is obtained and () = holds, i.e., in the same way that the principal branch of the log-gamma function is defined.
In mathematical physics, in particular electromagnetism, the Riemann–Silberstein vector [1] or Weber vector [2] [3] named after Bernhard Riemann, Heinrich Martin Weber and Ludwik Silberstein, (or sometimes ambiguously called the "electromagnetic field") is a complex vector that combines the electric field E and the magnetic field B.
In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by Sergei Godunov in 1959, [1] for solving partial differential equations. One can think of this method as a conservative finite volume method which solves exact, or approximate Riemann problems at each inter-cell boundary. In ...
The propagation speed of these two equations is equivalent to the propagation speed of sound. The fastest characteristic defines the Courant–Friedrichs–Lewy (CFL) condition, which sets the restriction for the maximum time step for which an explicit numerical method is stable. Generally as more conservation equations are used, more ...
In multivariable calculus, an initial value problem [a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to
In mathematics, the Riemann xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation. The function is named in honour of Bernhard Riemann .