{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T16:15:32Z","timestamp":1649175332888},"reference-count":19,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,1,1]]},"abstract":"<jats:title>Complex Function Differentiability<\/jats:title>\n        <jats:p>For a complex valued function defined on its domain in complex numbers the differentiability in a single point and on a subset of the domain is presented. The main elements of differential calculus are developed. The algebraic properties of differential complex functions are shown.<\/jats:p>","DOI":"10.2478\/v10037-009-0007-9","type":"journal-article","created":{"date-parts":[[2009,7,15]],"date-time":"2009-07-15T01:04:59Z","timestamp":1247619899000},"page":"67-72","source":"Crossref","is-referenced-by-count":2,"title":["Complex Function Differentiability"],"prefix":"10.2478","volume":"17","author":[{"given":"Chanapat","family":"Pacharapokin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroshi","family":"Yamazaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasunari","family":"Shidama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yatsuka","family":"Nakamura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"1","first-page":"121","article-title":"Complex sequences","volume":"1","author":"Agnieszka Banachowicz","year":"1993","journal-title":"Formalized Mathematics"},{"key":"2","first-page":"41","article-title":"The fundamental properties of natural numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"3","first-page":"91","article-title":"The ordinal numbers","volume":"1","author":"Grzegorz Bancerek","year":"1990","journal-title":"Formalized Mathematics"},{"key":"4","first-page":"507","article-title":"The complex numbers","volume":"3","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"5","first-page":"55","article-title":"Functions and their basic properties","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"6","first-page":"153","article-title":"Functions from a set to a set","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"7","first-page":"357","article-title":"Partial functions","volume":"2","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"8","first-page":"35","article-title":"Basic properties of real numbers","volume":"1","author":"Krzysztof Hryniewiecki","year":"1990","journal-title":"Formalized Mathematics"},{"key":"9","first-page":"273","article-title":"Convergent sequences and the limit of sequences","volume":"2","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"10","first-page":"471","article-title":"Monotone real sequences. Subsequences","volume":"3","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"11","first-page":"697","article-title":"Partial functions from a domain to a domain","volume":"4","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"12","first-page":"269","article-title":"Real sequences and basic operations on them","volume":"2","author":"Jaros\u0142aw Kotowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"13","first-page":"185","article-title":"Property of complex sequence and continuity of complex function","volume":"1","author":"Takashi Mitsuishi","year":"2001","journal-title":"Formalized Mathematics"},{"key":"14","first-page":"265","article-title":"Conjugate sequences, bounded complex sequences and convergent complex sequences","volume":"2","author":"Adam Naumowicz","year":"1997","journal-title":"Formalized Mathematics"},{"key":"15","first-page":"403","article-title":"Convergence and the limit of complex sequences. Series","volume":"3","author":"Yasunari Shidama","year":"1997","journal-title":"Formalized Mathematics"},{"key":"16","first-page":"329","article-title":"Binary operations applied to functions","volume":"2","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"17","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"18","first-page":"73","article-title":"Relations and their basic properties","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"},{"key":"19","first-page":"181","article-title":"Relations defined on sets","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/17\/2\/article-p67.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2009.17.issue-2\/v10037-009-0007-9\/v10037-009-0007-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:27:40Z","timestamp":1590852460000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-009-0007-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,1]]},"references-count":19,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/v10037-009-0007-9","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2009,1,1]]}}}