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The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π . However, it has some drawbacks (for example, it is computer memory -intensive) and therefore all record-breaking calculations for many years have used other ...
The standard Gaussian measure on . is a Borel measure (in fact, as remarked above, it is defined on the completion of the Borel sigma algebra, which is a finer structure);; is equivalent to Lebesgue measure: , where stands for absolute continuity of measures;
The Legendre pseudospectral method (based on Gauss-Lobatto points) has been implemented in flight [1] by NASA on several spacecraft through the use of the software, DIDO.The first flight implementation was on November 5, 2006, when NASA used DIDO to maneuver the International Space Station to perform the Zero Propellant Maneuver.
It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".
Just as the normal distribution is the maximum information entropy distribution for fixed values of the first moment and second moment (with the fixed zeroth moment = corresponding to the normalization condition), the q-Gaussian distribution is the maximum Tsallis entropy distribution for fixed values of these three moments.
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In statistics, a Gaussian random field (GRF) is a random field involving Gaussian probability density functions of the variables. A one-dimensional GRF is also called a Gaussian process.
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that