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Question Number 127214 by mohammad17 last updated on 27/Dec/20

$$whatisthevalueofandhowcancombute?$$$$$$$$erf\left(\pi \right)?$$

Answered by Olaf last updated on 27/Dec/20

$$\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi }}{\int }_0^x{e}^{-t^2}dt$$$$\left(\mathrm{used}\mathrm{in}\mathrm{probabilities}\mathrm{and}\mathrm{statistics}\right)$$$$\mathrm{erf}\left(\pi \right)=\frac{2}{\sqrt{\pi }}{\int }_0^{\pi }{e}^{-t^{2}dt}$$$$\mathrm{We}\mathrm{can}\mathrm{compute}:$$$$\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi }}\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^n}{(2n+1)n!}{x}^{2n+1}$$$$\mathrm{erf}\left(\pi \right)=\frac{2}{\sqrt{\pi }}\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^n}{(2n+1)n!}{\pi }^{2n+1}$$$$\mathrm{erf}\left(\pi \right)\approx 2\sqrt{\pi }-\frac{2{\pi }^{5/2}}{3}+\frac{{\pi }^{9/2}}{5}-\frac{{\pi }^{13/2}}{21}+o\left({\pi }^{17/2}\right)$$

Commented by mohammad17 last updated on 27/Dec/20

$$thankyousir$$

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