# Nodes and Weights of Gaussian quadrature (Select method) Calculator

## Calculates the nodes and weights of the Gaussian quadrature.(i.e. Gauss-Legendre, Gauss-Chebyshev 1st, Gauss-Chebyshev 2nd, Gauss-Laguerre, Gauss-Hermite, Gauss-Jacobi, Gauss-Lobatto and Gauss-Kronrod)

 kinds LegendreChebyshev 1stChebyshev 2ndLaguerreHermiteJacobiLobattoKronrod order n 23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 α β 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Gaussian\ quadrature\\\hspace{30} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\vspace{10}\hspace{20} Quadrature \hspace{30} interval \hspace{10} w(x) \hspace{30} polynomials\\\vspace{5}(1)\ Legendre \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\(2)\ Chebyshev\ 1st \hspace{5} (-1,\ 1) \hspace{10} {\large\frac{1}{\sqrt{1-x^2}}} \hspace{70} T_n(x) \\(3)\ Chebyshev\ 2nd \hspace{5} [-1,\ 1] \hspace{10} \sqrt{1-x^2} \hspace{65} U_n(x) \\(4)\ Laguerre \hspace{50} [0,\infty) \hspace{20} x^{\alpha} e^{-x} \hspace{65} L_n^\alpha (x) \\(5)\ Hermite \hspace{50} (-\infty,\infty) \hspace{10} e^{-x^2} \hspace{70} H_n (x) \\(6)\ Jacobi \hspace{75} (-1,\ 1) \hspace{10} (1-x)^{\alpha}(1+x)^{\beta} \hspace{5} J_n^{\alpha,\beta} (x) \\(7)\ Lobatto \hspace{60} [-1,\ 1] \hspace{25} 1 \hspace{80} P_{n-1}^' (x)\\(8)\ Kronrod \hspace{50} [-1,\ 1] \hspace{25} 1 \hspace{90} P_n(x)\\$

Nodes and Weights of Gaussian quadrature (Select method)
 [1-10] /22 Disp-Num5103050100200
[1]  2019/03/27 21:32   Male / 20 years old level / Elementary school/ Junior high-school student / Useful /
Purpose of use
calculation
[2]  2019/01/18 03:09   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
research (kinetic modelling)
[3]  2018/11/27 00:03   Male / 30 years old level / High-school/ University/ Grad student / Very /
Purpose of use
project
Comment/Request
good service
[4]  2018/09/10 21:51   Male / 30 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Implementation of orthogonal collocation
[5]  2018/07/28 12:44   Male / 20 years old level / An engineer / Useful /
Purpose of use
Building custom FEA codes. Need to implement Gaussian quadrature to evaluate element matrices, which involves integrating a constitutive matrix transformed to a shape function basis.
Comment/Request
In addition to the numerical values, analytical solutions would be nice to have. Maybe not for a production code, but very useful for more sophisticated prototyping and playing with ideas.
[6]  2018/07/13 17:48   Male / 40 years old level / A teacher / A researcher / Very /
Purpose of use
Scientific publications, Ill cite this website.
[7]  2018/06/23 11:32   Male / 20 years old level / A teacher / A researcher / Useful /
Purpose of use
Numerical integration.
[8]  2017/12/02 05:54   Male / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Studying for Numeric Calculus test
Comment/Request
Maybe show all the steps in the calculation to help people study
[9]  2016/07/15 14:40   Male / 60 years old level or over / High-school/ University/ Grad student / Very /
Purpose of use
Analysing a physics motion problem, to high precision, that cropped up in lab work.
Comment/Request
I am from Australia; why don't we teach Gaussian quadrature in this country? It is so superior to other methods!
[10]  2015/06/29 05:15   Female / 20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Computer Science course Assignment

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