Related

inf-limit-plot2d

f:n*(n-1)/2;

plot2d([f,n*n/2 ],[n,...

limit(f-n*n/2,n,inf);

Calculate

inf-sum

sum(k!/(2*k+1)!,k,0,i...

Calculate

inf-integrate-simpsum-sum

sum (i^2, i, 1, 7);

sum (a[i], i, 1, 7);

sum (a(i), i, 1, 7);

Calculate

inf-integrate-sin

integrate(sin(x)/x,x,...

Calculate

inf-limit

a:(3^n+5^n+7^n)^0.5;

limit (a,n,inf);

Calculate

inf-limit

''limit((Sin(n + 1)^2...

Calculate

inf-integrate-simpsum-sum

sum (i^2, i, 1, 7);

sum (a[i], i, 1, 7);

sum (a(i), i, 1, 7);

Calculate

inf-limit-sqrt

limit ((sqrt((n^2+2)-...

Calculate

inf-limit-plot2d

y: limit(((x-x^(2^n))...

plot2d(y, [x, 0.1, 0....

Calculate

inf-limit-sqrt

a:((-n+2)/sqrt(9*n^2+...

limit(a,n,inf);

Calculate

inf

Run Example
(%i1)integrate(log(x)/(x^2+(0.5)^2),x,0,inf);

rat: replaced 0.25 by 1/4 = 0.25

rat: replaced 0.25 by 1/4 = 0.25

rat: replaced 0.25 by 1/4 = 0.25

rat: replaced 0.25 by 1/4 = 0.25

rat: replaced 0.25 by 1/4 = 0.25
(%o1)                               4 false
(%i2) 
Run Example
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
limit((243*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)           +(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^6           -18*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^5           -9*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^4           +270*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^3           -486*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^2)           *(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^(-i-1)           /(-10206*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)            +14*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^6            -18*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^5            -810*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^4            +1620*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^3            +3645*(3*sqrt(5)/4-3^(3/2)*sqrt(5-sqrt(5))/2^(3/2)-9/4)^2+5832),i,inf);
(%o1)                                  0
(%i2) 

Help for Inf