# Gauss-Hermite quadrature Calculator

## Calculates the integral of the given function f(x) over the interval (-∞,∞) using Gauss-Hermite quadrature.

 $\normal Gauss-Hermite\ quadrature\\[10] {\large\int_{\small -\infty}^{\hspace{25}\small \infty}}e^{-x^2}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\ {\large\int_{\small -\infty}^{\hspace{25}\small \infty}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}e^{x_i^2}g(x_i)\\\vspace{20}$

 g(x)f(x) partition n23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The integrand f(x) is assumed to be analytic and non-periodic.$\normal Gaussian\ quadrature\\\hspace{10} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i), \ {\large\int_{\small a}^{\hspace{25}\small b}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Hermite\ quadrature\\\hspace{30} interval(a,b):\hspace{20} (-\infty,\infty)\\\hspace{30} w(x):\hspace{80} e^{-x^2}\\\hspace{30} polynomialsl:\hspace{10} H_n (x) \\$

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[1]  2013/01/07 07:20   Male / 50 years old level / Others / A little /
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A great page. Thank you. Miguel from Spain.

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