{"id":150,"date":"2024-02-22T12:54:07","date_gmt":"2024-02-22T17:54:07","guid":{"rendered":"https:\/\/sites.nd.edu\/joseph-heston\/?p=150"},"modified":"2024-02-22T12:56:45","modified_gmt":"2024-02-22T17:56:45","slug":"a-pseudogamma-function","status":"publish","type":"post","link":"https:\/\/sites.nd.edu\/joseph-heston\/2024\/02\/22\/a-pseudogamma-function\/","title":{"rendered":"A \u00a0Pseudogamma Function"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Does there exist a psuedogamma function that (when substituted into the Cauchy formula for repeated integration) yields a fractional Differintegral that equals (or approximates) the Gr\\&#8221;unwald-Letnikov derivative?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Riemann%E2%80%93Liouville_differintegral\">Riemann\u2013Liouville differintegral<\/a> and the\u00a0<a href=\"https:\/\/en.wikipedia.org\/w\/index.php?title=Caputo_differintegral&amp;action=edit&amp;redlink=1\">Caputo differintegral<\/a> are different, so you could use either process (or maybe both) to check for agreement. <\/p>\n\n\n\n<p class=\"has-large-font-size wp-block-paragraph\">A Follow-up Question:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Do these integrals yield the expected values in the trivial cases? (Eg: trig functions, polynomials, exp() or Mittag-Leffler, Guassian Distribution, etc.)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Does there exist a psuedogamma function that (when substituted into the Cauchy formula for repeated integration) yields a fractional Differintegral that equals (or approximates) the Gr\\&#8221;unwald-Letnikov derivative? The\u00a0Riemann\u2013Liouville differintegral and the\u00a0Caputo differintegral are different, so you could use either process (or maybe both) to check for agreement. A Follow-up Question: Do these integrals yield the [&hellip;]<\/p>\n","protected":false},"author":4053,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-150","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/posts\/150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/users\/4053"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/comments?post=150"}],"version-history":[{"count":2,"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/posts\/150\/revisions"}],"predecessor-version":[{"id":153,"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/posts\/150\/revisions\/153"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/media?parent=150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/categories?post=150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.nd.edu\/joseph-heston\/wp-json\/wp\/v2\/tags?post=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}