# Nodes and Weights of Gauss-Hermite Calculator

## Calculates the nodes and weights of the Gauss-Hermite quadrature.

 $\normal Gauss-Hermite\ quadrature\\ {\large\int_{\small -\infty}^{\hspace{25}\small \infty}}e^{-x^2}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\ nodes\hspace{30} x_i:\ the\ i-th\ zeros\ of\ H_n(x)\\\ weights\hspace{15} w_i={\large\frac{2^{n-1}n!\sqrt{\large\pi}}{[nH_{n-1}(x_i)]^2}}\\\vspace{20}$

 order n 23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100n=2,3,4,..,100 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Gaussian\ quadrature\\\hspace{10} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i), \ {\large\int_{\small a}^{\hspace{25}\small b}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Hermite\ quadrature\\\hspace{30} interval(a,b):\hspace{20} (-\infty,\infty)\\\hspace{30} w(x):\hspace{80} e^{-x^2}\\\hspace{30} polynomialsl:\hspace{10} H_n (x) \\$

Nodes and Weights of Gauss-Hermite
 [1-10] /14 Disp-Num5103050100200
[1]  2019/03/10 21:17   Male / 20 years old level / A teacher / A researcher / Useful /
Purpose of use
Design a filter.
Comment/Request
NaN
[2]  2018/10/30 15:16   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
Computations
[3]  2018/03/13 21:47   Female / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
Results can be easily verified for my course on Advanced Numerical Techniques.
[4]  2018/03/06 09:22   Male / 50 years old level / An office worker / A public employee / - /
Purpose of use
numerical integration
[5]  2017/12/13 07:33   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Project
[6]  2017/01/23 12:15   Male / 20 years old level / A teacher / A researcher / Very /
Purpose of use
Marginal likelihood computation
Comment/Request
[7]  2015/10/26 16:57   Male / 20 years old level / A teacher / A researcher / Very /
Purpose of use
Computation of expectations for functions of normally distributed variables.
[8]  2015/04/27 19:04   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
For spectral method
[9]  2015/01/31 04:48   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
need for computatuions
[10]  2014/11/22 06:29   Male / 60 years old level or over / An engineer / Very /
Purpose of use
Aircraft landing precision

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