## Details and Options

ResourceFunction["GeneralMiniMaxApproximation"] by default minimizes the maximum value of the relative error between the approximation and *expr*.

ResourceFunction["GeneralMiniMaxApproximation"][{*f*_{x},*f*_{y},*g*},{*t*,{*t*_{0},*t*_{1}},*m*,*n*},*x*] computes the error using a factor of *g*. In this case, the mini-max approximation returned by ResourceFunction["GeneralMiniMaxApproximation"] is the rational function *h*[*x*] that minimizes the maximum value of the quantity (*f*_{y}-*h*[*f*_{x}])/*g*.

ResourceFunction["GeneralMiniMaxApproximation"] returns {*abscissa*,{*approximation*,*maxerror*}}, where *abscissa* is a list of the abscissas where the relative error is a local maximum, *approximation* is the rational approximant, and *maxerror* is the global maximum of the relative error.

When an approximation is given as the second argument of ResourceFunction["GeneralMiniMaxApproximation"], it must have the same form as the result returned by ResourceFunction["GeneralMiniMaxApproximation"].

ResourceFunction["GeneralMiniMaxApproximation"] takes the same options as MiniMaxApproximation.

In the "Derivatives" option, a list of derivatives must give derivatives for both parts of the parametrically defined function.