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Online Algebra Calculator
Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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![plot2d([erf(x), x*2/sqrt(%pi)/(1+1/2.9*x^2-1/120*x^4)],[x,-3,3]);](http://maxima-online.org/plot.html?g=p468524960.png&t=img&db=r-1207661697)
![plot2d([sqrt(%pi)*1/2*erf(x)+x-(1/x)-sqrt(%pi)*1/2*erf(1)],[x,-30,30]);](http://maxima-online.org/plot.html?g=p-866701008.png&t=img&db=r-271755865)
![plot2d([erf(x), x*2/sqrt(%pi)/(1+1/3*x^2-1/140*x^4)],[x,-3,3]);](http://maxima-online.org/plot.html?g=p1133639288.png&t=img&db=r-1129373365)
erf
Run Example
(%i1)f(x):=exp(-x^2); 2 (%o1) f(x) := exp(- x ) (%i2) tex( expand( integrate( (x-y-l)*f(x), x, l+y, inf) )); $${{\sqrt{\pi}\,y\,\mathrm{erf}\left(y+l\right)}\over{2}}+{{\sqrt{\pi }\,l\,\mathrm{erf}\left(y+l\right)}\over{2}}+{{e^{-y^2-2\,l\,y-l^2} }\over{2}}-{{\sqrt{\pi}\,y}\over{2}}-{{\sqrt{\pi}\,l}\over{2}}$$ (%o2) false (%i3) tex(integrate( expand( integrate( (x-y-l)*f(x), x, l+y, inf) * f(y)),y, -inf,inf)); $$\int_{-\infty }^{\infty }{{{\sqrt{\pi}\,y\,e^ {- y^2 }\, \mathrm{erf}\left(y+l\right)}\over{2}}+{{\sqrt{\pi}\,l\,e^ {- y^2 } \,\mathrm{erf}\left(y+l\right)}\over{2}}-{{\sqrt{\pi}\,y\,e^ {- y^2 }}\over{2}}-{{\sqrt{\pi}\,l\,e^ {- y^2 }}\over{2}}+{{e^{-2\,y^2-2\, l\,y-l^2}}\over{2}}\;dy}$$ (%o3) false (%i4) integrate( expand( integrate( (x-y-l)*f(x), x, l+y, inf) * f(y)),y, -inf,inf); inf 2 2 / - y - y [ sqrt(%pi) y %e erf(y + l) sqrt(%pi) l %e erf(y + l) (%o4) I (----------------------------- + ----------------------------- ] 2 2 / - inf 2 2 2 2 - y - y - 2 y - 2 l y - l sqrt(%pi) y %e sqrt(%pi) l %e %e - ------------------ - ------------------ + ---------------------) dy 2 2 2 (%i5) integrate( y*exp(-y^2), y, -inf,inf); (%o5) 0 (%i6) integrate( exp(-y^2)*erf(y+l),y,-inf,inf ); inf / 2 [ - y (%o6) I %e erf(y + l) dy ] / - inf (%i7) integrate( y*exp(-y^2),y,-inf,inf); (%o7) 0 (%i8) integrate( exp(-y^2),y,-inf,inf); (%o8) sqrt(%pi) (%i9) integrate( exp(-(y+l)^2),y,-inf,inf); (%o9) sqrt(%pi) (%i10) romberg(exp(-y^2)*erf(y+l),y,-inf,inf); 2 - y (%o10) romberg(%e erf(y + l), y, - 1.0 inf, inf) (%i11)
Run Example
G(x):=0.5*(1+erf(x/sqrt(2))); x (%o1) G(x) := 0.5 (1 + erf(-------)) sqrt(2) (%i2) Q(x,m,d):= G((x-m)/d); x - m (%o2) Q(x, m, d) := G(-----) d (%i3)
Run Example
eq1:exp(-x^2); 2 - x (%o1) %e (%i2) integrate(eq1,x); sqrt(%pi) erf(x) (%o2) ---------------- 2 (%i3) erf(2); (%o3) erf(2) (%i4)
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