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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 n=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] /13 Disp-Num5103050100200
[1]  2018/10/30 15:16   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
Computations
[2]  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.
[3]  2018/03/06 09:22   Male / 50 years old level / An office worker / A public employee / - /
Purpose of use
numerical integration
[4]  2017/12/13 07:33   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Project
[5]  2017/01/23 12:15   Male / 20 years old level / A teacher / A researcher / Very /
Purpose of use
Marginal likelihood computation
Comment/Request
Would be nice to download the roots/quadrature weights as a TSV file.
[6]  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.
[7]  2015/04/27 19:04   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
For spectral method
[8]  2015/01/31 04:48   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
need for computatuions
[9]  2014/11/22 06:29   Male / 60 years old level or over / An engineer / Very /
Purpose of use
Aircraft landing precision
[10]  2014/11/19 07:19   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
verification of own code

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