Approximations | Analytic number theory | Theorems in analysis | Asymptotic analysis | Gamma and related functions
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: where the big O notation means that, for all sufficiently large values of , the difference between and will be at most proportional to the logarithm. In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to use instead the binary logarithm, giving the equivalent form The error term in either base can be expressed more precisely as , corresponding to an approximate formula for the factorial itself,Here the sign means that the two quantities are asymptotic, that is, that their ratio tends to 1 as tends to infinity. The following version of the bound holds for all , rather than only asymptotically: (Wikipedia).
Probability 101c: Stirling's approximation
(C) 2012 David Liao lookatphysics.com CC-BY-SA Replaces unscripted drafts Approximation for n! when n is large Comparison with integral of natural logarithm
From playlist Probability, statistics, and stochastic processes
Stirling's Incredible Approximation // Gamma Functions, Gaussians, and Laplace's Method
We prove Stirling's Formula that approximates n! using Laplace's Method. ►Get my favorite, free calculator app for your phone or tablet: MAPLE CALCULATOR: https://www.maplesoft.com/products/maplecalculator/download.aspx?p=TC-9857 ►Check out MAPLE LEARN for your browser to make beautiful gr
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Gaussian Integral 9 Stirling Way
Welcome to the awesome 12-part series on the Gaussian integral. In this series of videos, I calculate the Gaussian integral in 12 different ways. Which method is the best? Watch and find out! In this video, I use Stirling's formula to 'prove' the Gaussian integral, namely I show that in t
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Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
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This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
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Polynomial approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
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Right hand riemann sum approximation
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Thermodynamics 4b - Entropy and the Second Law II
We compare the reversibility of the Carnot cycle to the irreversibility of the Stirling cycle and find that they may be accounted for by the constancy or increase of transferred heat divided by temperature. We then consider how conservation laws, including the fundamental laws of mechanics
From playlist Thermodynamics
Physics 32.5 Statistical Thermodynamics (8 of 39) Stirling's Approximation: Summery
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 In this video I will use Stirling's approximation to find thermodynamic probability. Next video in the polar coordinates series can
Thermodynamics 3b - Energy and the First Law II
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From playlist Thermodynamics
Physics 32.5 Statistical Thermodynamics (11 of 39) Number of Microstates Analyzed N=100
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 In this video I will analyze the number of microstates when N=100. Next video in the polar coordinates series can be seen at: http:/
ROBINSON HOT AIR stirling ENGINE by TUBALCAIN
We have here a model hot air engine based on the famous ROBINSON patent. Shown running.
From playlist STIRLING HOT AIR ENGINES
PHILIPS STIRLING CYCLE GENERATOR
PHILIPS MP1002 CA in near original condition Beta configuration, bellcrank linkage
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How to use left hand riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
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Polynomial approximation of functions (part 2)
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From playlist Calculus