{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T17:48:57Z","timestamp":1725558537656},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642141270"},{"type":"electronic","value":"9783642141287"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-14128-7_1","type":"book-chapter","created":{"date-parts":[[2010,6,29]],"date-time":"2010-06-29T10:45:36Z","timestamp":1277808336000},"page":"1-12","source":"Crossref","is-referenced-by-count":7,"title":["The Challenges of Multivalued \u201cFunctions\u201d"],"prefix":"10.1007","author":[{"given":"James H.","family":"Davenport","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"1_CR1","unstructured":"Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. US Government Printing Office (1964)"},{"key":"1_CR2","unstructured":"Apostol, T.M.: Calculus, 1st edn., vol.\u00a0I. Blaisdell (1961)"},{"key":"1_CR3","doi-asserted-by":"crossref","unstructured":"Beaumont, J.C., Bradford, R.J., Davenport, J.H., Phisanbut, N.: Adherence is Better Than Adjacency. In: Kauers, M. (ed.) Proceedings ISSAC 2005, pp. 37\u201344 (2005)","DOI":"10.1145\/1073884.1073892"},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/s00200-007-0052-y","volume":"18","author":"J.C. Beaumont","year":"2007","unstructured":"Beaumont, J.C., Bradford, R.J., Davenport, J.H., Phisanbut, N.: Testing Elementary Function Identities Using CAD. AAECC\u00a018, 513\u2013543 (2007)","journal-title":"AAECC"},{"key":"1_CR5","unstructured":"Bourbaki, N.: Th\u00e9orie des Ensembles. In: Diffusion CCLS (1970)"},{"key":"1_CR6","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1023\/A:1016007415899","volume":"36","author":"R.J. Bradford","year":"2002","unstructured":"Bradford, R.J., Corless, R.M., Davenport, J.H., Jeffrey, D.J., Watt, S.M.: Reasoning about the Elementary Functions of Complex Analysis. Annals of Mathematics and Artificial Intelligence\u00a036, 303\u2013318 (2002)","journal-title":"Annals of Mathematics and Artificial Intelligence"},{"key":"1_CR7","volume-title":"Theory of functions of a complex variable","author":"C. Carath\u00e9odory","year":"1958","unstructured":"Carath\u00e9odory, C.: Theory of functions of a complex variable. Chelsea Publ., New York (1958)"},{"key":"1_CR8","volume-title":"Elementary Theory of Analytic Functions of One or Several Complex Variables","author":"H. Cartan","year":"1973","unstructured":"Cartan, H.: Elementary Theory of Analytic Functions of One or Several Complex Variables. Addison-Wesley, Reading (1973)"},{"issue":"2","key":"1_CR9","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1145\/362001.362023","volume":"34","author":"R.M. Corless","year":"2000","unstructured":"Corless, R.M., Davenport, J.H., Jeffrey, D.J., Watt, S.M.: According to Abramowitz and Stegun. SIGSAM Bulletin\u00a034(2), 58\u201365 (2000)","journal-title":"SIGSAM Bulletin"},{"key":"1_CR10","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1006\/jsco.2002.0551","volume":"34","author":"J.H. Davenport","year":"2002","unstructured":"Davenport, J.H.: Equality in computer algebra and beyond. J. Symbolic Comp.\u00a034, 259\u2013270 (2002)","journal-title":"J. Symbolic Comp."},{"key":"1_CR11","volume-title":"Applied and Computational Complex Analysis I","author":"P. Henrici","year":"1974","unstructured":"Henrici, P.: Applied and Computational Complex Analysis I. Wiley, Chichester (1974)"},{"key":"1_CR12","volume-title":"Methods of Mathematical Physics","author":"H. Jeffreys","year":"1956","unstructured":"Jeffreys, H., Jeffreys, B.: Methods of Mathematical Physics, 3rd edn. Cambridge University Press, Cambridge (1956)","edition":"3"},{"key":"1_CR13","unstructured":"Kahan, W.: Branch Cuts for Complex Elementary Functions. In: Iserles, A., Powell, M.J.D. (eds.) The State of Art in Numerical Analysis, pp. 165\u2013211 (1987)"},{"key":"1_CR14","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0747-7171(08)80026-0","volume":"9","author":"D. Lazard","year":"1990","unstructured":"Lazard, D., Rioboo, R.: Integration of Rational Functions - Rational Computation of the Logarithmic Part. J. Symbolic Comp.\u00a09, 113\u2013115 (1990)","journal-title":"J. Symbolic Comp."},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1006\/jsco.1997.0112","volume":"24","author":"T. Mulders","year":"1997","unstructured":"Mulders, T.: A note on subresultants and the Lazard\/Rioboo\/Trager formula in rational function integration. J. Symbolic Comp.\u00a024, 45\u201350 (1997)","journal-title":"J. Symbolic Comp."},{"key":"1_CR16","doi-asserted-by":"publisher","first-page":"743","DOI":"10.2307\/2373917","volume":"101","author":"R.H. Risch","year":"1979","unstructured":"Risch, R.H.: Algebraic Properties of the Elementary Functions of Analysis. Amer. J. Math.\u00a0101, 743\u2013759 (1979)","journal-title":"Amer. J. Math."},{"key":"1_CR17","doi-asserted-by":"crossref","unstructured":"Ritt, J.F.: Differential Algebra. In: American Mathematical Society Colloquium Proceedings, vol.\u00a0XXXIII (1950)","DOI":"10.1090\/coll\/033"},{"key":"1_CR18","unstructured":"Wiedijk, F.: The De Bruijn Factor (2000), \n                    \n                      http:\/\/www.cs.kun.nl\/~freek\/notes\/factor.pdf"}],"container-title":["Lecture Notes in Computer Science","Intelligent Computer Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-14128-7_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T12:19:08Z","timestamp":1619785148000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-14128-7_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642141270","9783642141287"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-14128-7_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}