(%i1) integrate(sin(x^2)/(x^2),x,1,inf);
defint: integral is divergent.
This used to just return the integral as a nounform. Numerical approximation says it's about 0.2862504407259549. Thanks!
What version are you using? The current version returns
-%i*gamma_incomplete(-1,2*%i)/2+%i*gamma_incomplete(-1,-2*%i)/2+1/2
This is approximately .6734567682657728. quad_qagi also says the integral is approximately 0.67335.
Marking this as pending/worksforme
I was using 5.25.0.
And
(%i3) quad_qagi(sin(x^2)/(x^2),x,1,inf); ***MESSAGE FROM ROUTINE DQAGI IN LIBRARY SLATEC. ***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED * ABNORMAL RETURN * ERROR NUMBER = 1 * ***END OF MESSAGE
(%o3) [.2852680980196833, .007186678748743569, 5985, 1]
And Wolfram Alpha gives, for input
integrate(sin(x^2)/x^2,x,1,inf)
sqrt(pi/2) (1-2 C(sqrt(2/pi)))+sin(1)~~0.285737
where C is a Fresnel integral.
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According to Laurent Fousse, it was caused by commit 59775311e53ef8a8fb5a3ad067a6c1cc153075d2 (see http://trac.sagemath.org/sage_trac/ticket/11737\)
Seems to be caused by the following problem with limit:
(%i2) limit( gamma_incomplete(-1/2, -%i*x^2), x, inf); (%o2) gamma_incomplete(-1/2,infinity)
Fixed by adding case for complex infinity to routine simplim%gamma_incomplete in gamma.lisp.
(%i2) limit( gamma_incomplete(-1/2, -%i*x^2), x, inf); (%o2) 0 (%i3) integrate(sin(x^2)/(x^2),x,1,inf); (%o3) %i*gamma_incomplete(-1/2,%i)/2^(5/2) -gamma_incomplete(-1/2,%i)/2^(5/2)-%i*gamma_incomplete(-1/2,-%i)/2^(5/2) -gamma_incomplete(-1/2,-%i)/2^(5/2) (%i4) float(%); (%o4) -.1767766952966368*(.2733129188747918*%i-.5348723621187728)*%i +.1767766952966368*(-.2733129188747918*%i-.5348723621187728)*%i -.1767766952966368*(.2733129188747918*%i-.5348723621187728) -.1767766952966368*(-.2733129188747918*%i-.5348723621187728) (%i5) rectform(%); (%o5) .2857366463228523
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What version are you using? The current version returns
-%i*gamma_incomplete(-1,2*%i)/2+%i*gamma_incomplete(-1,-2*%i)/2+1/2
This is approximately .6734567682657728. quad_qagi also says the integral is approximately 0.67335.
Marking this as pending/worksforme
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I was using 5.25.0.
And
(%i3) quad_qagi(sin(x^2)/(x^2),x,1,inf);
***MESSAGE FROM ROUTINE DQAGI IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 1
*
***END OF MESSAGE
(%o3) [.2852680980196833, .007186678748743569, 5985, 1]
And Wolfram Alpha gives, for input
integrate(sin(x^2)/x^2,x,1,inf)
sqrt(pi/2) (1-2 C(sqrt(2/pi)))+sin(1)~~0.285737
where C is a Fresnel integral.
View and moderate all "bugs Discussion" comments posted by this user
Mark all as spam, and block user from posting to "Bugs"
View and moderate all "bugs Discussion" comments posted by this user
Mark all as spam, and block user from posting to "Bugs"
According to Laurent Fousse, it was caused by commit 59775311e53ef8a8fb5a3ad067a6c1cc153075d2 (see http://trac.sagemath.org/sage_trac/ticket/11737\)
Seems to be caused by the following problem with limit:
(%i2) limit( gamma_incomplete(-1/2, -%i*x^2), x, inf);
(%o2) gamma_incomplete(-1/2,infinity)
Fixed by adding case for complex infinity to
routine simplim%gamma_incomplete in gamma.lisp.
(%i2) limit( gamma_incomplete(-1/2, -%i*x^2), x, inf);
(%o2) 0
(%i3) integrate(sin(x^2)/(x^2),x,1,inf);
(%o3) %i*gamma_incomplete(-1/2,%i)/2^(5/2)
-gamma_incomplete(-1/2,%i)/2^(5/2)-%i*gamma_incomplete(-1/2,-%i)/2^(5/2)
-gamma_incomplete(-1/2,-%i)/2^(5/2)
(%i4) float(%);
(%o4) -.1767766952966368*(.2733129188747918*%i-.5348723621187728)*%i
+.1767766952966368*(-.2733129188747918*%i-.5348723621187728)*%i
-.1767766952966368*(.2733129188747918*%i-.5348723621187728)
-.1767766952966368*(-.2733129188747918*%i-.5348723621187728)
(%i5) rectform(%);
(%o5) .2857366463228523