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Two cases arise: The first case is theoretical: when you know all the coefficients then you take certain limits and find the precise radius of convergence.; The second case is practical: when you construct a power series solution of a difficult problem you typically will only know a finite number of terms in a power series, anywhere from a couple of terms to a hundred terms.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, [1] nearest-neighbor distribution function [2] or nearest neighbor distribution [3] is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned ...
A minimum off-route altitude (MORA) provides a quick way for an aircraft pilot to read the minimum altitude required for terrain and obstacle clearance. MORAs give at least 1,000 feet altitude clearance above terrain and obstacles such as radio masts, and 2,000 feet where the terrain and obstacles exceed 5,000 feet. [1]
By measuring the orbit distance between the reference point and the point calculated with low precision, it can be detected that it is not possible to calculate the point correctly, and the calculation can be stopped. These incorrect points can later be re-calculated e.g. from another closer reference point.
In asymptotic analysis in general, one sequence () that converges to a limit is said to asymptotically converge to with a faster order of convergence than another sequence () that converges to in a shared metric space with distance metric | |, such as the real numbers or complex numbers with the ordinary absolute difference metrics, if
Here an algorithm is developed to determine this distance, based on the analytic results for the distance of closest approach of ellipses in 2D, which can be implemented numerically. Details are given in publications. [14] [15] Subroutines are provided in two formats: Fortran90 [16] and C. [17] The algorithm consists of three steps.
Calculate the squared scalar distance of the second observation, by taking the dot product of the position vector of the second observation: = where R 2 2 {\displaystyle {R_{2}}^{2}} is the squared distance of the second observation