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(*defineyourfavoritefunction*)​​f[x_]:=x(x-0.5)(x-0.7)​​(*definetheLandaukernel*)​​L[n_,x_]:=(1-x^2)^n;​​(*computetheconstanttomakesureintegralisone*)​​c[n_]:=1/NIntegrate[L[n,x],{x,-1,1}];​​(*reviseLandaukernel*)​​l[n_,x_]:=c[n]*L[n,x];​​(*computeconvolution.notelimitsofintegration!*)​​(*theyarenotfrom-ooto+oo.whydoesitwork?*)​​h[n_,x_]:=NIntegrate[f[y]*l[n,x-y],{y,0,1}]​​(*pickavalueofnandplottheresults*)​​n=20;​​Plot[{f[x],h[20,x]},{x,0,1}]