Ask Question
For questions regarding the theory and evaluation of the Gaussian integral, also known as the Euler–Poisson integral is the integral of the Gaussian function $~e^{−x^2}~$ over the entire real line. . It is named after the German mathematician Carl Friedrich Gauss.
768 questions- Bountied 0
- Unanswered
- Frequent
- Score
- Unanswered (my tags)
Integration: Gauss quadrature formula of the Integral $\int_{-1}^1f(x)\sqrt{|x|}dx$
I want to find the formula for the Gauss quadrature that integrate the Integral $\int_{-1}^1f(x)\sqrt{|x|}\, dx$ exactly for every cubic polynomial $f$. What exactly do we have to do here? Is $\sqrt{|... integration numerical-methods gaussian-integral quadrature- 13
How to evaluate the following Gaussian double integral
I am trying to evaluate the following gaussian double integral $P=\int dB dA \exp(-\dfrac{Q}{2\sigma^2})$ where $Q=\sum_{i=1}^{N} (d_i-A \exp(-\alpha t_i)-B\exp(-\beta t_i))^2$ The result should yield ... integration probability-distributions gaussian-integral laplace-method- 1
Evaluation of power times gaussian multivariable integral
In the context of evaluating the propagation of a flattened Gaussian beam, the following integral appears: \begin{equation} \int (\mathbf x^T \mathbf F \mathbf x)^n \exp \left [ - \mathbf x^T \mathbf ... integration multivariable-calculus definite-integrals indefinite-integrals gaussian-integral- 63
Integral of the product of two gaussian
Let's suppose that we have $p_1$ that is the pdf of a gaussian distribution 1 and $p_2$ that is the pdf of a gaussian distribution 2. The two gaussian distributions are independent. I need to find ... probability integration statistics gaussian-integral- 111
Definite Integral of $\text{exp}(-(\sum_i |x_i|^a)^b)$
I would like to solve: $$\int_{\mathbf{R}^n} \text{exp}\left(-\left(\sum_i |x_i|^a\right)^b\right)\;dx_1...dx_n$$ I have no idea how to tackle this integral. For the special case of $a=1$ I obtained ... multivariable-calculus definite-integrals normal-distribution gamma-function gaussian-integral- 13
gaussian integral without the error function
here is my attempt.is it correct? $$I = \int e^{-x^2}dx$$ let $u = e^{-x^2}$ and $v=x$ then : $$I = xe^{-x^2} - \int -2x^2e^{-x^2} dx ; J = \int -x^2e^{-x^2}dx$$ here is where I'm in doubt am I alowed ... calculus integration gaussian-integral- 41
Why the dummy variable $y$ in the calculation of the gaussian integral as follows?
I don't understand why you have to use a different variable when squared the first integral? It is commonly glossed over to explain this. gaussian-integral- 353
Integrating bi-variate Gaussian density with respect to their correlation coefficient
I'm wondering if there is any literature that deals with the integral of the following type $$ \int \dfrac{1}{2\pi\sqrt{1-\rho^2}} \cdot \exp(-\dfrac{(a^2+b^2+2\rho ab)}{2(1-\rho^2)}) \cdot d\rho $$ ... integration probability-distributions gaussian-integral- 66
Gaussian integral in 3rd dimensions
I have been wondering about computing $(1/3)!$ and using the Gamma function. After substituting for $x=t^{\frac{1}{3}}$, I got $\int_{0}^{\infty}e^{-x^{3}}dx$. May I know if there is any way to ... integration definite-integrals gamma-function gaussian-integral- 13
How to prove or calculate $E[\int_{t_{i-1}}^{t_i} e^{-μ({t_i}-s)}\sigma B_s |x_{t_{i-1}}]=0$?
$B_s$ is brownian motion. Because $\int_{t_{i-1}}^{t_i} e^{-μ({t_i} -s)}\sigma dB_s $ has a Brownian component, it is normally distributed with the mean zero according to Taylor & Karin 1998 's ... calculus stochastic-calculus brownian-motion gaussian-integral- 1
Evaluating the Gaussian-like integrals $\int dx\, x^{-n} \exp(-(x-b)^2)$
Is there a known form for indefinite Gaussian integrals of the form $$\int dx\, x^{-n}\exp(-(x-b)^2) $$ where $n$ is a positive integer and $b$ is some constant? Mathematica cannot solve integrals of ... calculus integration indefinite-integrals gaussian-integral- 93
Very fast but inaccurate estimations of multivariate Gaussian integral over a hypercube
$\def\Z{\mathbb{Z}}\def\R{\mathbb{R}}\def\A{\mathcal{A}}\def\N{\mathcal{N}}$ I'm working on 4D positive real values, i.e. $\R^4_{\geq 0}$, where it is gridized with hypercubes of side length $a > 0$... multivariable-calculus gaussian-integral- 5,414
Simplify the multiplication of Two Gaussian Function
I am reading this article The derivation at equation (9) confused me. At equation (8), it's $$ NE=E_{AB}\... gaussian-integral- 175
Application of Gaussian Integration Technique
In order to solve the Gaussian integral $\int\limits_{-\infty}^{\infty} e^{-x^2}\,dx$, we set this value to $I$, square, and evaluate the following double integral in polar form ($I=\sqrt{\pi}$). Can ... multivariable-calculus gaussian-integral- 45
Jacobian in multidimensional Gaussian integral
For the first integral shown in: reference for multidimensional gaussian integral It is mentioned that the Jacobian is 1, how is this the case? By following the calculation I found it to be $det(diag(... statistics gaussian-integral gaussian- 63
15 30 50 per page12345…52 Next
