## #1508 Bug in Limit of a function

closed
5
2008-10-14
2008-10-10
No

Try

(%i1) kill(all);
(eq0) done
(%i1) assume_pos:true;
(eq1) true
(%i2) (declare(n,integer),assume(sigma>0,equal(n-1, 0)));
(eq2) [sigma>0,equal(n,1)]
(%i3) f(x):=(sqrt(2)/(2*sqrt(%pi)*sqrt(sigma)))*exp(-(x^2/(2*sigma)));
(eq3) f(x):=sqrt(2)/(2*sqrt(%pi)*sqrt(sigma))*exp(-x^2/(2*sigma))
(%i4) integrate(f(x),x,minf,inf);
(eq4) 1
(%i5) integrate(x^2*f(x), x, minf, inf)-(integrate(x*f(x), x, minf, inf))^2;
(eq5) sigma
(%i6) integrate(x*f(a*x-b^2),x,minf,inf);
(eq6) b^2/a^2
(%i7) limit(integrate((a*x^3+b*x^2+c*x+d)*f(x^n), x, minf, inf), sigma,0);
(eq7) 0
(%i8) limit(integrate((a*x^3+b*x^2+c*x+d)*f(x), x, minf, inf), sigma,0);
(eq8) d

Output 7 is 0 and output 8 is d. They can't both be right since input 2 declares n=1, so they are equivilent.

Rich Hennessy

Maxima version: 5.16.3
Maxima build date: 22:48 8/24/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

## Discussion

• Dan Gildea - 2008-10-14

Duplicate of [ 707253 ] limit(x^y,x,0) (y=0) => 0.
Fixed in simp.lisp 1.58 and limit.lisp 1.56.

• Dan Gildea - 2008-10-14
• status: open --> closed
• assigned_to: nobody --> dgildea

No, thanks