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erfc-exp-integrate-pi-sqrt-taylor

f(x) := exp(-x*x);

t(x) := taylor(f(x), ...

i(x) := sqrt(%pi)/2-i...

Calculate

erfc-exp-integrate-pi-plot2d-sqrt-taylor
plot2d([i(x), g(x)], [x, 0, 2]);

f(x) := exp(-x*x);

t(x) := taylor(f(x), ...

i(x) := 1-integrate(t...

Calculate

erfc-plot2d
plot2d([0.5*erfc(0.326512*(15.85-x)),[discrete, [12.9, 13.1, 14.4, 14.9, 15.3, 16.5, 17.1, 17.8, 18.0, 19.4],[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]]],[x,10,20],[style,lines,points], [color, black, black],[point_type, circle]);

plot2d([0.5*erfc(0.32...

Calculate

erfc-taylor

taylor(erfc(x),x,0,10);

Calculate

erfc-plot2d
plot2d([0.5*erfc(0.326512*(15.85-x)),[discrete, [12.9, 13.1, 14.4, 14.9, 15.3, 16.5, 17.1, 17.8, 18.0, 19.4],[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]]],[x,10,21],[y,0,1.1],[style,lines,points], [color, black, black],[point_type, dot],[axes,true],[box,false],[legend, "", ""]);

plot2d([0.5*erfc(0.32...

Calculate

erfc-exp-factor-taylor

taylor(exp(-x^2)*(erf...

factor(2176);

Calculate

erfc-plot2d
plot2d([0.5*erfc(0.326512*(15.85-x))],[x,10,20]);

plot2d([0.5*erfc(0.32...

Calculate

erfc-plot2d
plot2d([0.5*erfc(0.326512*(15.85-x)),[discrete, [12.9, 13.1, 14.4, 14.9, 15.3, 16.5, 17.1, 17.8, 18.0, 19.4],[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]]],[x,10,21],[y,0,1.1],[style,lines,points], [color, black, black],[point_type, bullet],[axes,true],[legend, "", ""]);

plot2d([0.5*erfc(0.32...

Calculate

erfc-exp-integrate-plot2d-taylor
plot2d([-i(x), g(x)], [x, 0, 2]);

f(x) := exp(-x*x);

t(x) := taylor(f(x), ...

i(x) := integrate(t(x...

Calculate

erfc-float

a:2;

float(erfc(2));

Calculate

erfc

Run Example
(%i1)assume(x>
0);
(%o1)                               [x > 0]
(%i2) f(x):=integrate(1/sqrt(-1+exp(x)*erfc(sqrt(x)) + 2*sqrt(x/%pi)),x);
                                              1
(%o2) f(x) := integrate(----------------------------------------------, x)
                                                                  x
                        sqrt(- 1 + exp(x) erfc(sqrt(x)) + 2 sqrt(---))
                                                                 %pi
(%i3) define(f1(x),diff(f(x),x,1));
                                           1
(%o3)          f1(x) := ---------------------------------------
                                             x   2 sqrt(x)
                        sqrt(erfc(sqrt(x)) %e  + --------- - 1)
                                                 sqrt(%pi)
(%i4) f1(0.01);
                                      1
(%o4)                 ----------------------------------
                              0.2
                      sqrt(--------- - 0.10354302003087)
                           sqrt(%pi)
(%i5) 
Run Example
a:2;
(%o1)                                  2
(%i2) float(erfc(2));
(%o2)                         0.0046777349810473
(%i3) 
Run Example
a:2;
(%o1)                                  2
(%i2) b:1;
(%o2)                                  1
(%i3) erfc (z);
(%o3)                               erfc(z)
(%i4) 

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