The Function command returns the exact function from a POLYINTERP structure.

If the Function command is used on a POLYINTERP structure whose exact function was not originally specified, an exception will be raised.

The POLYINTERP structure is created using the PolynomialInterpolation command or the CubicSpline command.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$\mathrm{xy}≔\left[\left[0\,4.0\right]\,\left[0.5\,0\right]\,\left[1.0\,-2.0\right]\,\left[1.5\,0\right]\,\left[2.0\,1.0\right]\,\left[2.5\,0\right]\,\left[3.0\,-0.5\right]\right]$

$\mathrm{xy}≔\left[\left[0\,4.0\right]\,\left[0.5\,0\right]\,\left[1.0\,\mathrm{-2.0}\right]\,\left[1.5\,0\right]\,\left[2.0\,1.0\right]\,\left[2.5\,0\right]\,\left[3.0\,\mathrm{-0.5}\right]\right]$

$\mathrm{p1}≔\mathrm{PolynomialInterpolation}\left(\mathrm{xy}\,\mathrm{function}=2^{2-x}\cos \left(\mathrm{\pi }x\right)\,\mathrm{method}=\mathrm{lagrange}\,\mathrm{extrapolate}=\left[0.25\,0.75\,1.25\right]\,\mathrm{errorboundvar}='\mathrm{\xi }'\right)\:$

$\mathrm{Function}\left(\mathrm{p1}\right)$

$2^{2-x}\cos \left(\mathrm{\pi }x\right)$

$\mathrm{plot}\left(\mathrm{Function}\left(\mathrm{p1}\right)\,x=0..3\right)$