{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:53:30Z","timestamp":1776794010520,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"276","license":[{"start":{"date-parts":[[2012,4,12]],"date-time":"2012-04-12T00:00:00Z","timestamp":1334188800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Under general conditions, the equation\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"g left-parenthesis x comma y right-parenthesis equals 0\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>g<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>y<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">g(x,y) = 0<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    implicitly defines\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"y\">\n                        <mml:semantics>\n                          <mml:mi>y<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">y<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    locally as a function of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"x\">\n                        <mml:semantics>\n                          <mml:mi>x<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">x<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In this article, we express divided differences of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"y\">\n                        <mml:semantics>\n                          <mml:mi>y<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">y<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in terms of bivariate divided differences of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"g\">\n                        <mml:semantics>\n                          <mml:mi>g<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">g<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , generalizing a recent result on divided differences of inverse functions.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02486-5","type":"journal-article","created":{"date-parts":[[2011,4,12]],"date-time":"2011-04-12T07:27:41Z","timestamp":1302593261000},"page":"2185-2195","source":"Crossref","is-referenced-by-count":1,"title":["Divided differences of implicit functions"],"prefix":"10.1090","volume":"80","author":[{"given":"Georg","family":"Muntingh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Floater","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2011,4,12]]},"reference":[{"key":"1","first-page":"46","article-title":"Divided differences","volume":"1","author":"de Boor, Carl","year":"2005","journal-title":"Surv. 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Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"4","article-title":"A Chain Rule for Multivariate Divided Differences","author":"Floater, Michael S.","year":"2009"},{"issue":"6","key":"5","first-page":"697","article-title":"On the divided difference form of Fa\u00e0 di Bruno\u2019s formula. II","volume":"25","author":"Wang, Xinghua","year":"2007","journal-title":"J. Comput. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0254-9409","issn-type":"print"},{"key":"6","first-page":"359","article-title":"Note sur une nouvelle formule de calcul diff\u00e9rentiel","volume":"1","author":"Fa\u00e0 di Bruno,Cavaliere Francesco","year":"1857","journal-title":"Quarterly J. Pure Appl. Math."},{"issue":"3","key":"7","doi-asserted-by":"publisher","first-page":"217","DOI":"10.2307\/2695352","article-title":"The curious history of Fa\u00e0 di Bruno\u2019s formula","volume":"109","author":"Johnson, Warren P.","year":"2002","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1090\/S0002-9947-96-01501-2","article-title":"A multivariate Fa\u00e0 di Bruno formula with applications","volume":"348","author":"Constantine, G. M.","year":"1996","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"9","article-title":"Implicit higher derivatives, and a formula of Comtet and Fiolet","author":"Wilde, Tom","year":"2008"},{"key":"10","first-page":"249","article-title":"Sur les d\u00e9riv\u00e9es successives d\u2019une fonction implicite","volume":"278","author":"Comtet, Louis","year":"1974","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. A","ISSN":"https:\/\/id.crossref.org\/issn\/0302-8429","issn-type":"print"},{"key":"11","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-2196-8","volume-title":"Advanced combinatorics","author":"Comtet, Louis","year":"1974","ISBN":"https:\/\/id.crossref.org\/isbn\/9027704414"},{"key":"12","series-title":"Cambridge Studies in Advanced Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511609589","volume-title":"Enumerative combinatorics. Vol. 2","volume":"62","author":"Stanley, Richard P.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0521560691"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02486-5\/S0025-5718-2011-02486-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02486-5\/S0025-5718-2011-02486-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:57:35Z","timestamp":1776790655000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02486-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,12]]},"references-count":12,"journal-issue":{"issue":"276","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["S0025-5718-2011-02486-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2011-02486-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2011,4,12]]}}}