Someone at my university reported the following Mathematica 7 bug to me and I thought I would share it with all of you in case someone was interested or could offer insight that we don’t have.\u00a0 Needless to say this has been reported to Wolfram via the official channels and I am sure that it will be sorted out soon.<\/p>\n
If you do<\/p>\n
Integrate[k^2 (k^2 – 1)\/((k^2 – 1)^2 + x^2)^(3\/2), {k, 0, Infinity},Assumptions -> x > 0]<\/p>\n
you get<\/p>\n
EllipticK[(2*x)\/(-I + x)]\/(2*Sqrt[-1 – I*x])<\/p>\n
Which is complex for all x whereas the integrand is purely real.\u00a0 As a\u00a0 particular example let us put x=2.\u00a0 Evaluating numerically:<\/p>\n
NIntegrate[k^2 (k^2 – 1)\/((k^2 – 1)^2 + 2^2)^(3\/2), {k, 0, Infinity}]<\/p>\n
gives<\/p>\n
0.706094<\/p>\n
But if I plug x=2 into the symbolic result given earlier<\/p>\n
N[EllipticK[(2*x)\/(-I + x)]\/(2*Sqrt[-1 – I*x]) \/.x->2]<\/p>\n
Then I get<\/p>\n
-5.35054*10^-17 + 0.568541 I<\/p>\n
Which is obvioulsy incorrect.\u00a0 Would someone with a copy of Maple 12 mind seeing what that makes of this integral please?\u00a0 Extra kudos to anyone who can do it by hand!<\/p>\n","protected":false},"excerpt":{"rendered":"
Someone at my university reported the following Mathematica 7 bug to me and I thought I would share it with all of you in case someone was interested or could offer insight that we don’t have.\u00a0 Needless to say this has been reported to Wolfram via the official channels and I am sure that it […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,8],"tags":[],"class_list":["post-578","post","type-post","status-publish","format-standard","hentry","category-math-software","category-mathematica"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-9k","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/578","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=578"}],"version-history":[{"count":4,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/578\/revisions"}],"predecessor-version":[{"id":582,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/578\/revisions\/582"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}