# Nodes and Weights of Gauss-Laguerre Calculator

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

 $\normal Gauss-Laguerre\ quadrature\\ {\large\int_{\small 0}^{\hspace{25}\small \infty}}x^{\alpha}e^{-x}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\\ nodes\hspace{30} x_i:\ the\ i-th\ zeros\ of\ L_n^\alpha(x)\\\ weights\hspace{15} w_i={\large\frac{\Gamma(n+\alpha+1)x_i}{n![(n+1)L^\alpha_{n+1}(x_i)]^2}}\\$

 order n 23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100n=2,3,4,..,100 α 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Gaussian\ quadrature\\\hspace{10} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i), \ {\large\int_{\small a}^{\hspace{25}\small b}}g(x)dx\simeq{\large\sum_{\small i=1}^{n}}{\large\frac{w_{i}}{w(x_i)}}g(x_i)\\Gauss-Laguerre\ quadrature\\\hspace{30} interval(a,b):\hspace{20} [0,\infty)\\\hspace{30} w(x):\hspace{80} x^{\alpha} e^{-x}\\\hspace{30} polynomialsl:\hspace{10} L_n^\alpha (x)\\$

Nodes and Weights of Gauss-Laguerre
 [1-5] /5 Disp-Num5103050100200
[1]  2015/02/15 22:47   Male / 50 years old level / A teacher / A researcher / Very /
Comment/Request
Is teh code public ? I would like to see it as I am interested to see if it is ok for n>100 and possibliy adapt it.
Thnaks
[2]  2015/02/11 09:38   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
numerically solving an initial value problem of a hyperbolic 4x4-system of PDE-s
[3]  2013/10/18 20:26   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
Checking precision of gauss-laguerre nodes and weights at 38 digits.
They are good at quad-precision( 35 digits)
Comment/Request
the display on screen truncates the third column of this calculation due
to lack of page space. In such cases can you extend the page or shift some
columns to another page?
However I tried "copy and paste" of the table to another editor and there I
was able to see all the columns in full.
Thank you
[4]  2012/02/28 01:52   Male / 30 years old level / A student / Very /
Comment/Request
I can integrate the Gauss-Laguerre Integral with an alpha < -1 (for example alpha = -1.8) but I cannot obtain weights!
[5]  2011/08/24 13:11   Male / 30 years old level / A teacher / A researcher / Very /
Purpose of use
Lecture for students.
Comment/Request
That is a great page.

Sending completion

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