{"id":4554,"date":"2024-01-16T11:21:01","date_gmt":"2024-01-16T19:21:01","guid":{"rendered":"https:\/\/bendwavy.org\/wp\/?p=4554"},"modified":"2024-01-16T11:21:01","modified_gmt":"2024-01-16T19:21:01","slug":"taylor-series-of-integral-of-exponential-of-fourier-series","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=4554","title":{"rendered":"Taylor series of integral of exponential of Fourier series"},"content":{"rendered":"

I have experimented with integrals of<\/p>\n

exp(i\u00b7f(t))<\/p><\/blockquote>\n

where ”f(t)” is a polynomial. I express these integrals as Taylor series, which are not hard to generate. Now I’d like to try<\/p>\n

f(t) = a\u00b7t + \u03a3bk<\/sub>\u00b7sin(k\u00b7t)<\/p><\/blockquote>\n

and I have a horrid feeling that the Taylor series will be a nightmare!<\/p>\n","protected":false},"excerpt":{"rendered":"

I have experimented with integrals of exp(i\u00b7f(t)) where ”f(t)” is a polynomial. I express these integrals as Taylor series, which are not hard to generate. Now I’d like to try f(t) = a\u00b7t + \u03a3bk\u00b7sin(k\u00b7t) and I have a horrid … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[72],"tags":[],"class_list":["post-4554","post","type-post","status-publish","format-standard","hentry","category-curve-fitting"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/4554","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4554"}],"version-history":[{"count":1,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/4554\/revisions"}],"predecessor-version":[{"id":4632,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/4554\/revisions\/4632"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4554"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4554"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}