# Associated Laguerre polynomial (chart) Calculator

## Calculates a table of the associated Laguerre polynomial Lnα(x) and draws the chart.

 n n=0,1,2,... α [ initial value x increment repetition ]
 $\normal Associated\ Laguerre\ polinomial\ L_n^\alpha(x)\\[10](1)\ xy''+(\alpha+1-x)y'+ny=0\\\hspace{25} y=L_n^\alpha(x)\\(2)\ {\large\frac{e^{-{\normal\frac{xt}{1-t}}}}{(1-t)^{\alpha+1}}}={\large\sum_{\small n=0}^{\small\infty}}L_n(x)t^n\\(3)\hspace{5}{\large\int_{\tiny 0}^{\hspace{25}\tiny \infty}}L_n^\alpha(x)L_m^\alpha(x)e^{-x}x^\alpha dx={\large\frac{(n+\alpha)!}{n!}}\delta_{mn}\\(4)\ L_n^\alpha(x)=(-1)^\alpha{\large\frac{d^\alpha}{dx^\alpha}}L_{n+\alpha}(x)\\\hspace{65}={\large\frac{e^xx^{-\alpha}}{n!}\frac{d^n}{dx^n}}(e^{-x}x^{n+\alpha})\\[10](5)\ L_n^\alpha(x)={\large\frac{(\alpha+1)_n}{n!}}{}_{\small 1}F_{\small 1}(-n;\alpha+1;x)\\$

Associated Laguerre polynomial (chart)
 [0-0] / 0 Disp-Num5103050100200
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