{"action":"created","issue":{"url":"https://api.github.com/repos/rodluger/starry/issues/98","repository_url":"https://api.github.com/repos/rodluger/starry","labels_url":"https://api.github.com/repos/rodluger/starry/issues/98/labels{/name}","comments_url":"https://api.github.com/repos/rodluger/starry/issues/98/comments","events_url":"https://api.github.com/repos/rodluger/starry/issues/98/events","html_url":"https://github.com/rodluger/starry/issues/98","id":331658411,"node_id":"MDU6SXNzdWUzMzE2NTg0MTE=","number":98,"title":"Evaluating `I_v` for `k^2 > 1`","user":{"login":"rodluger","id":9323819,"node_id":"MDQ6VXNlcjkzMjM4MTk=","avatar_url":"https://avatars3.githubusercontent.com/u/9323819?v=4","gravatar_id":"","url":"https://api.github.com/users/rodluger","html_url":"https://github.com/rodluger","followers_url":"https://api.github.com/users/rodluger/followers","following_url":"https://api.github.com/users/rodluger/following{/other_user}","gists_url":"https://api.github.com/users/rodluger/gists{/gist_id}","starred_url":"https://api.github.com/users/rodluger/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rodluger/subscriptions","organizations_url":"https://api.github.com/users/rodluger/orgs","repos_url":"https://api.github.com/users/rodluger/repos","events_url":"https://api.github.com/users/rodluger/events{/privacy}","received_events_url":"https://api.github.com/users/rodluger/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":1,"created_at":"2018-06-12T16:15:45Z","updated_at":"2018-06-12T17:17:14Z","closed_at":null,"author_association":"OWNER","body":"For integer `v`, the expression for `I_v` in the `k^2 > 1` limit\r\n![image](https://user-images.githubusercontent.com/9323819/41302924-a214f8c8-6e20-11e8-8674-a276c899bf27.png)\r\nis just a ratio of Gamma functions:\r\n![image](https://user-images.githubusercontent.com/9323819/41302916-9be8cbc8-6e20-11e8-98f1-c1b5b400f95b.png)\r\nfor which [efficient, accurate algorithms](https://www.boost.org/doc/libs/1_60_0/libs/math/doc/html/math_toolkit/sf_gamma/gamma_ratios.html) exist. I'm going to pre-tabulate these up to some large value of `v` at compile-time and compute higher values as needed in run-time."},"comment":{"url":"https://api.github.com/repos/rodluger/starry/issues/comments/396666979","html_url":"https://github.com/rodluger/starry/issues/98#issuecomment-396666979","issue_url":"https://api.github.com/repos/rodluger/starry/issues/98","id":396666979,"node_id":"MDEyOklzc3VlQ29tbWVudDM5NjY2Njk3OQ==","user":{"login":"rodluger","id":9323819,"node_id":"MDQ6VXNlcjkzMjM4MTk=","avatar_url":"https://avatars3.githubusercontent.com/u/9323819?v=4","gravatar_id":"","url":"https://api.github.com/users/rodluger","html_url":"https://github.com/rodluger","followers_url":"https://api.github.com/users/rodluger/followers","following_url":"https://api.github.com/users/rodluger/following{/other_user}","gists_url":"https://api.github.com/users/rodluger/gists{/gist_id}","starred_url":"https://api.github.com/users/rodluger/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rodluger/subscriptions","organizations_url":"https://api.github.com/users/rodluger/orgs","repos_url":"https://api.github.com/users/rodluger/repos","events_url":"https://api.github.com/users/rodluger/events{/privacy}","received_events_url":"https://api.github.com/users/rodluger/received_events","type":"User","site_admin":false},"created_at":"2018-06-12T17:17:14Z","updated_at":"2018-06-12T17:17:14Z","author_association":"OWNER","body":"Well, since `I_v` doesn't depend on `b` or `r` when `ksq >= 1`, the derivative is always zero, no? Shouldn't be a problem for autodiff."}}
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