# Hermite polynomial (chart) Calculator

## Calculates a table of the Hermite polynomial Hn(x) and draws the chart.

 n=0,1,2,...
[ initial value x
increment
 repetition ]
 $\normal Hermite\ polinomial\ H_n(x)\\[10](1)\ y''-2xy'+ny=0,\hspace{20}y=H_n(x)\\[10](2)\ {\large e^{2xt-t^2}}={\large\sum_{n=0}^{\infty}\frac{H_n(x)}{n!}}t^n\$$3)\hspace{5}{\large\int_{\tiny -\infty}^{\hspace{25}\tiny \infty}}H_n(x)H_m(x){\large e^{-x^2}}dx={\large 2^nn!\sqrt{n}\delta_{mn}}\\(4)\ H_n(x)\\\hspace{10}=2^n{\large\sqrt{\pi}}\({\large\frac{{}_{\tiny 1}F_{\tiny 1} (-\frac{n}{2};\frac{1}{2};x^2)}{\Gamma(\frac{1-n}{2})}}-{\large\frac{{}_{\tiny 1}F_{\tiny 1} (\frac{1-n}{2};\frac{3}{2};x^2)2x}{\Gamma(-\frac{n}{2})}}$$\\$

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