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• Gaussian_integral abstract "The Gaussian integral, also known as the Euler–Poisson integral is the integral of the Gaussian function e−x2 over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss. The integral is:This integral has a wide range of applications. For example, with a slight change of variables it is used to compute the normalizing constant of the normal distribution. The same integral with finite limits is closely related both to the error function and the cumulative distribution function of the normal distribution. In physics this type of integral appears frequently, for example, in quantum mechanics, to find the probability density of the ground state of the harmonic oscillator, also in the path integral formulation, and to find the propagator of the harmonic oscillator, we make use of this integral. Although no elementary function exists for the error function, as can be proven by the Risch algorithm, the Gaussian integral can be solved analytically through the methods of calculus. That is, there is no elementary indefinite integral for but the definite integral can be evaluated.The Gaussian integral is encountered very often in physics and numerous generalizations of the integral are encountered in quantum field theory.".
• Gaussian_integral thumbnail E%5E(-x%5E2).svg?width=300.
• Gaussian_integral wikiPageExternalLink Generalization.
• Gaussian_integral wikiPageID "567580".
• Gaussian_integral wikiPageRevisionID "606728464".
• Gaussian_integral hasPhotoCollection Gaussian_integral.
• Gaussian_integral title "Gaussian Integral".
• Gaussian_integral urlname "GaussianIntegral".
• Gaussian_integral subject Category:Articles_containing_proofs.
• Gaussian_integral subject Category:Gaussian_function.
• Gaussian_integral subject Category:Integrals.
• Gaussian_integral subject Category:Theorems_in_analysis.
• Gaussian_integral type Abstraction100002137.
• Gaussian_integral type Calculation105802185.
• Gaussian_integral type Cognition100023271.
• Gaussian_integral type Communication100033020.
• Gaussian_integral type HigherCognitiveProcess105770664.
• Gaussian_integral type Integral106015505.
• Gaussian_integral type Integrals.
• Gaussian_integral type Message106598915.
• Gaussian_integral type ProblemSolving105796750.
• Gaussian_integral type Process105701363.
• Gaussian_integral type Proposition106750804.
• Gaussian_integral type PsychologicalFeature100023100.
• Gaussian_integral type Statement106722453.
• Gaussian_integral type Theorem106752293.
• Gaussian_integral type TheoremsInAnalysis.
• Gaussian_integral type Thinking105770926.
• Gaussian_integral comment "The Gaussian integral, also known as the Euler–Poisson integral is the integral of the Gaussian function e−x2 over the entire real line. It is named after the German mathematician and physicist Carl Friedrich Gauss. The integral is:This integral has a wide range of applications. For example, with a slight change of variables it is used to compute the normalizing constant of the normal distribution.".
• Gaussian_integral label "Fehlerintegral".
• Gaussian_integral label "Gaussian integral".
• Gaussian_integral label "Integral Gaussiana".
• Gaussian_integral label "Integral de Gauss".
• Gaussian_integral label "Integrale di Gauss".
• Gaussian_integral label "Intégrale de Gauss".
• Gaussian_integral label "Гауссов интеграл".
• Gaussian_integral label "تكامل غاوسي".
• Gaussian_integral label "ガウス積分".
• Gaussian_integral label "高斯积分".
• Gaussian_integral sameAs Gaussův_integrál.
• Gaussian_integral sameAs Fehlerintegral.
• Gaussian_integral sameAs Integral_de_Gauss.
• Gaussian_integral sameAs Intégrale_de_Gauss.
• Gaussian_integral sameAs Integrale_di_Gauss.
• Gaussian_integral sameAs ガウス積分.
• Gaussian_integral sameAs 가우스_적분.
• Gaussian_integral sameAs Integral_Gaussiana.
• Gaussian_integral sameAs m.02qv2w.
• Gaussian_integral sameAs Q1060321.
• Gaussian_integral sameAs Q1060321.
• Gaussian_integral sameAs Gaussian_integral.
• Gaussian_integral wasDerivedFrom Gaussian_integral?oldid=606728464.
• Gaussian_integral depiction E%5E(-x%5E2).svg.
• Gaussian_integral isPrimaryTopicOf Gaussian_integral.