{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T22:33:46Z","timestamp":1785969226665,"version":"3.56.0"},"reference-count":15,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[2003,8,1]],"date-time":"2003-08-01T00:00:00Z","timestamp":1059696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,8,1]],"date-time":"2003-08-01T00:00:00Z","timestamp":1059696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3638,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics Letters"],"published-print":{"date-parts":[[2003,8]]},"DOI":"10.1016\/s0893-9659(03)90026-7","type":"journal-article","created":{"date-parts":[[2003,12,19]],"date-time":"2003-12-19T05:57:50Z","timestamp":1071813470000},"page":"975-979","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":32,"title":["A short proof of the generalized Fa\u00e0 di bruno's formula"],"prefix":"10.1016","volume":"16","author":[{"given":"L.Hern\u00e1ndez","family":"Encinas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.Mu\u00f1oz","family":"Masqu\u00e9","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0893-9659(03)90026-7_BIB1","first-page":"359","article-title":"Note sur une nouvelle formule de calcul diff\u00e9rentiel","volume":"1","author":"deBruno","year":"1856","journal-title":"Quart. J. Math."},{"issue":"4","key":"10.1016\/S0893-9659(03)90026-7_BIB2","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1023\/A:1007323118991","article-title":"Krichever maps, Fa \u00e0 di Bruno polynomials, and cohomology in KP theories","volume":"42","author":"Falqui","year":"1997","journal-title":"Lett. Math. Phys."},{"key":"10.1016\/S0893-9659(03)90026-7_BIB3","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1214\/aoms\/1177705059","article-title":"The multivariate saddlepoint method and chi-squared for the multinomial distribution","volume":"32","author":"Good","year":"1961","journal-title":"Annals of Mathematical Statistics"},{"key":"10.1016\/S0893-9659(03)90026-7_BIB4","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/S0378-4754(96)00040-7","article-title":"Iterated derivatives of the output of a nonlinear dynamic system and Fa\u00e1 di Bruno formula","volume":"42","author":"Hespel","year":"1996","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/S0893-9659(03)90026-7_BIB5","first-page":"1","article-title":"The multi-dimensional Fa\u00e0 diBruno formula","volume":"45","author":"Kawagishi","year":"1999","journal-title":"Rep. Res. Inst. Sci. Technol. Nihon Univ."},{"key":"10.1016\/S0893-9659(03)90026-7_BIB6","first-page":"340","article-title":"Applications of Fa\u00e0, di Bruno's formula in mathematical statistics","volume":"62","author":"Lukacs","year":"1955","journal-title":"Amer. Math. Monthly"},{"issue":"2","key":"10.1016\/S0893-9659(03)90026-7_BIB7","first-page":"215","article-title":"Some strange identities related to Fa\u00e0 di Bruno formula","volume":"21","author":"Zhao","year":"2001","journal-title":"J. Math. Res. Exposition"},{"issue":"6","key":"10.1016\/S0893-9659(03)90026-7_BIB8","first-page":"559","article-title":"From Ford to Fa\u00e0","volume":"108","author":"Flanders","year":"2001","journal-title":"Amer. Math. Monthly"},{"issue":"2","key":"10.1016\/S0893-9659(03)90026-7_BIB9","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1090\/S0002-9947-96-01501-2","article-title":"A multivariate Faa di Bruno formula with applications","volume":"348","author":"Constantine","year":"1996","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0893-9659(03)90026-7_BIB10","first-page":"159","article-title":"Formulae for high derivatives of composite functions","volume":"83","author":"Fraenkel","year":"1978"},{"key":"10.1016\/S0893-9659(03)90026-7_BIB11","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1006\/jcta.1996.0107","article-title":"A q-analogue of Fa\u00e0 diBruno's formula","volume":"76","author":"Johnson","year":"1996","journal-title":"J. Combin. Theory, Ser. A"},{"key":"10.1016\/S0893-9659(03)90026-7_BIB12","doi-asserted-by":"crossref","first-page":"331","DOI":"10.2307\/2310518","article-title":"On the n-derivative of composite functions","volume":"63","author":"McKiernen","year":"1956","journal-title":"Amer. Math. Monthly"},{"issue":"7","key":"10.1016\/S0893-9659(03)90026-7_BIB13","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1155\/S0161171200002970","article-title":"Generalization of the formula of Fa\u00e0 di Bruno for a composite function with a vector argument","volume":"24","author":"Mishkov","year":"2000","journal-title":"Internat. J. Math. & Math. Sci."},{"key":"10.1016\/S0893-9659(03)90026-7_BIB14","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1090\/S0002-9904-1946-08621-8","article-title":"Derivatives of composite functions","volume":"52","author":"Riordan","year":"1946","journal-title":"Bull. Amer. Math. Soc."},{"key":"10.1016\/S0893-9659(03)90026-7_BIB15","first-page":"423","article-title":"A new look at Faa' de Bruno's formula for higher derivatives of composite functions and the expression of some intrinsic derivatives","volume":"40","author":"Ronga","year":"1983"}],"container-title":["Applied Mathematics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965903900267?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965903900267?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:09:57Z","timestamp":1760238597000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893965903900267"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,8]]},"references-count":15,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2003,8]]}},"alternative-id":["S0893965903900267"],"URL":"https:\/\/doi.org\/10.1016\/s0893-9659(03)90026-7","relation":{},"ISSN":["0893-9659"],"issn-type":[{"value":"0893-9659","type":"print"}],"subject":[],"published":{"date-parts":[[2003,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A short proof of the generalized Fa\u00e0 di bruno's formula","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0893-9659(03)90026-7","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}