The question is how correctly to do AQ and how to correctly handle > improper integrals. What I would appreciate is some real numerical > analysis or pointers to where we can do the research to support what > Ajo is asking us to commit. Just running tests on one problem > instance demonstrates nothing. I asked politely several times and > got no response. >
Page 170 of numerical recipes third edition. "The basic trick for improper integrals is to make a change of variables to eliminate the singularity or to map an infinite range of integration to a finite one." See also http://www.gnu.org/software/gsl/manual/html_node/QAGI-adaptive-integration-on-infinite-intervals.html#QAGI-adaptive-integration-on-infinite-intervals I hope this can convince people...
