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The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...
is the definition of the Schwarzschild radius for an object of mass , so the Schwarzschild metric may be rewritten in the alternative form: d s 2 = ( 1 − r s r ) − 1 d r 2 + r 2 ( d θ 2 + sin 2 θ d ϕ 2 ) − c 2 ( 1 − r s r ) d t 2 {\displaystyle ds^{2}=\left(1-{\frac {r_{s}}{r}}\right)^{-1}dr^{2}+r^{2}(d\theta ^{2}+\sin ^{2}\theta ...
A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass. The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon , which is situated at the Schwarzschild radius ( r s {\displaystyle r_{\text{s ...
Deutsch: Dieses Dokument listet 20323 Symbole und die dazugehörigen LaTeX-Befehle auf. Manche Symbole sind in jedem LaTeX-2ε-System verfügbar; andere benötigen zusätzliche Schriftarten oder Pakete, die nicht notwendig in jeder Distribution mitgeliefert werden und daher selbst installiert werden müssen.
for the first derivative, for the second derivative, for the third derivative, and for the nth derivative. When f is a function of several variables, it is common to use "∂", a stylized cursive lower-case d, rather than "D". As above, the subscripts denote the derivatives that are being taken.
An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".
Christoffel symbols satisfy the symmetry relations = or, respectively, =, the second of which is equivalent to the torsion-freeness of the Levi-Civita connection. The contracting relations on the Christoffel symbols are given by
Thus, the Schwarzian derivative precisely measures the degree to which a function fails to be a Möbius transformation. [1] If g is a Möbius transformation, then the composition g o f has the same Schwarzian derivative as f; and on the other hand, the Schwarzian derivative of f o g is given by the chain rule