# Complex Analysis/Elliptic functions

An elliptic function is a function $f\in M(\mathbb {C} )$ such that there exists a lattice $L\subset \mathbb {C}$ a basis $\{w_{1},w_{2}\}$ of which satisfies
$\forall z\in \mathbb {C} :f(z+w_{1})=f(z)=f(z+w_{2})$ .
{"ft_lang_label":"__label__en","ft_lang_prob":0.8218641,"math_prob":0.9999827,"size":327,"snap":"2020-45-2020-50","text_gpt3_token_len":69,"char_repetition_ratio":0.21981424,"word_repetition_ratio":0.68085104,"special_character_ratio":0.18042813,"punctuation_ratio":0.056603774,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999979,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,3,null,4,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-30T15:42:31Z\",\"WARC-Record-ID\":\"<urn:uuid:9eb5fdb4-1707-4902-8dcf-692602e01a28>\",\"Content-Length\":\"29680\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ab75bb88-f75f-476e-b958-a5947cc9e56e>\",\"WARC-Concurrent-To\":\"<urn:uuid:e207dd98-841e-4074-a0f2-69d8f6f4a01a>\",\"WARC-IP-Address\":\"208.80.154.224\",\"WARC-Target-URI\":\"https://en.wikibooks.org/wiki/Complex_Analysis/Elliptic_functions\",\"WARC-Payload-Digest\":\"sha1:PXJNCDL3WEZ2E55E5J4IBXRAHOAVV7CO\",\"WARC-Block-Digest\":\"sha1:APJ3XJHTTSD6XJOD4GTFNGJZCELVUEYW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141216175.53_warc_CC-MAIN-20201130130840-20201130160840-00167.warc.gz\"}"}