Open rtoy opened 1 month ago
Imported from SourceForge on 2024-07-09 11:16:44 Created by robert_dodier on 2023-11-24 18:59:04 Original: https://sourceforge.net/p/maxima/bugs/4213/#81a5
Imported from SourceForge on 2024-07-09 11:16:47 Created by robert_dodier on 2023-11-24 18:59:04 Original: https://sourceforge.net/p/maxima/bugs/4213/#0157
For the record, the equivalent Maxima-specific formulation is
integrate (sin(x)/x, x, -M, M);
limit (%, x, M, inf);
Not clear to me where the error is entering the picture, whether integrate
is calling the limit code and the error is in limit
, or if integrate
is getting mixed up on its own.
integrate
has trouble with related problems if 0 is in the interval of integration, but it seems to be okay if 0 is excluded, e.g.
assume (M1 > 0);
foo: integrate (sin(x)/x, x, M1, inf);
ev (foo, M1 = 1/100, numer, expand);
seems okay (it's approximately pi/2) but
limit (foo, M1, 0, plus);
provokes "unfamiliar singularity".
Imported from SourceForge on 2024-07-09 11:16:51 Created by willisbl on 2023-12-30 13:18:50 Original: https://sourceforge.net/p/maxima/bugs/4213/#1843
Incidentally:
OK:
(%i1) integrate(sin(x)/x,x,minf,inf);
(%o1) %pi
OK:
(%i2) defint(sin(x)/x,x,minf,inf);
(%o2) %pi
Not OK:
(%i3) ldefint(sin(x)/x,x,minf,inf);
(%o3) 0
A better antiderivative for integrate(sin(x)/x,x,-M,M)
is expintegral_si(M) - expintegral_si(-M)
. And
(%i26) limit(expintegral_si(M) - expintegral_si(-M),M,inf);
(%o26) %pi
Imported from SourceForge on 2024-07-09 11:16:54 Created by rtoy on 2023-12-30 16:46:19 Original: https://sourceforge.net/p/maxima/bugs/4213/#bacf
I think that antiderivative is better than the one we return today which involves gamma_incomplete(0,%i*x)
. The occurrence of %i
is kind of messy looking.
Imported from SourceForge on 2024-07-09 11:16:42 Created by zzoo on 2023-11-17 03:15:28 Original: https://sourceforge.net/p/maxima/bugs/4213
This is from comment: https://sourceforge.net/p/maxima/mailman/message/51782153/ One can check this against other CAS systems with sage: sage: integrate(sin(x)/x, x,-M,M,algorithm='maxima').limit(M=infinity) 0 sage: integrate(sin(x)/x, x,-M,M,algorithm='giac').limit(M=infinity) pi sage: integrate(sin(x)/x, x,-M,M,algorithm='fricas').limit(M=infinity) pi