Nodes and Weights of Gauss-Kronrod Calculator

Calculates the nodes and weights of the Gauss-Kronrod quadrature.

 $\normal Gauss-Kronrod\ quadrature\\[10] {\large\int_{\small -1}^{\hspace{25}\small 1}}f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\{\large\int_a^{\hspace{25}b}}f(x)dx\simeq{\large\frac{b-a}{2}\sum_{\small i=1}^{n}}w_{i}f({\large\frac{b-a}{2}}x_i+{\large\frac{b+a}{2}})\\\vspace{20}$
 display Kronrod xi wi + Gauss wi order n 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99  n=3,5,7,..   (odd)
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Gaussian\ quadrature\\\hspace{20} {\large\int_{\small a}^{\hspace{25}\small b}}w(x)f(x)dx\simeq{\large\sum_{\small i=1}^{n}}w_{i}f(x_i)\\Gauss-Kronrod\ quadrature\\\hspace{30} interval(a,b):\hspace{20} [-1,\ 1]\\\hspace{30} w(x):\hspace{80} 1\\\hspace{30} polynomialsl:\hspace{10} P_n (x)\\$

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