{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:42:02Z","timestamp":1740123722318,"version":"3.37.3"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s11075-021-01071-3","type":"journal-article","created":{"date-parts":[[2021,4,24]],"date-time":"2021-04-24T07:26:52Z","timestamp":1619249212000},"page":"1183-1214","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Blossoming and Hermite-Pad\u00e9 approximation for hypergeometric series"],"prefix":"10.1007","volume":"88","author":[{"given":"Rachid","family":"Ait-Haddou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8919-6844","authenticated-orcid":false,"given":"Marie-Laurence","family":"Mazure","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"key":"1071_CR1","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s11075-016-0242-4","volume":"76","author":"R Ait-Haddou","year":"2017","unstructured":"Ait-Haddou, R.: q-Blossoming and Hermite-Pad\u00e9 approximants to the q-exponential function. Numer. Algo. 76, 53\u201366 (2017)","journal-title":"Numer. Algo."},{"key":"1071_CR2","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1016\/j.amc.2015.05.068","volume":"266","author":"R Ait-Haddou","year":"2015","unstructured":"Ait-Haddou, R., Goldman, R.: Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials. App. Math Comp. 266, 267\u2013276 (2015)","journal-title":"App. Math Comp."},{"key":"1071_CR3","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10208-016-9334-8","volume":"18","author":"R Ait-Haddou","year":"2018","unstructured":"Ait-Haddou, R., Mazure, M.-L.: The fundamental blossoming inequality in Chebyshev Spaces I: applications to schur functions. Found. Comp. Math. 18, 135\u2013158 (2018)","journal-title":"Found. Comp. Math."},{"key":"1071_CR4","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1093\/qmath\/15.1.375","volume":"15","author":"A Baker","year":"1964","unstructured":"Baker, A.: Rational approximations to $\\sqrt [3]{2}$ and other algebraic numbers. Quart. J. Math. 15, 375\u2013383 (1964)","journal-title":"Quart. J. Math."},{"key":"1071_CR5","volume-title":"Essentials of Pad\u00e9 Approximants","author":"GA Baker","year":"1975","unstructured":"Baker, G.A.: Essentials of Pad\u00e9 Approximants. Academic Press, New York (1975)"},{"key":"1071_CR6","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/BF02075469","volume":"4","author":"PB Borwein","year":"1988","unstructured":"Borwein, P.B.: Pad\u00e9 approximants for the q-elementary functions. Constr. Approx. 4, 391\u2013402 (1988)","journal-title":"Constr. Approx."},{"key":"1071_CR7","volume-title":"Oeuvres","author":"C Brezinski","year":"1984","unstructured":"Brezinski, C., Pad\u00e9, H.: Oeuvres. Albert Blanchard, Paris (1984)"},{"key":"1071_CR8","doi-asserted-by":"crossref","unstructured":"de Bruin, M.G.: Some convergence results in simultaneous rational approximation to the set of hypergeometric functions $\\{{~}_{1}\\!F_{1}(1; C_{i}; Z)\\}_{i=1}^{n}$. In: Pad\u00e9 Approximation and Its Applications, Lecture Notes in Mathematics, vol. 1071, pp 12\u201333. Springer, Berlin (1984)","DOI":"10.1007\/BFb0099607"},{"key":"1071_CR9","doi-asserted-by":"crossref","unstructured":"de Bruin, M. G.: Simultaneous rational approximation to some q-hypergeometric functions. In: Nonlinear Numerical Methods and Rational Approximation, Math. Appl., vol. 43, pp 135\u2013142. Reidel, Dordrecht (1988)","DOI":"10.1007\/978-94-009-2901-2_7"},{"key":"1071_CR10","first-page":"445","volume":"58","author":"GV Chudnovsky","year":"1979","unstructured":"Chudnovsky, G.V.: Pad\u00e9 approximations to the generalized hypergeometric functions. J. Math. Pures Appl. 58, 445\u2013476 (1979)","journal-title":"J. Math. Pures Appl."},{"key":"1071_CR11","doi-asserted-by":"crossref","unstructured":"Chudnovsky, D.V., Chudnovsky, G.V.: Pad\u00e9 and rational approximations to systems of functions and their arithmetic applications. In: Lecture Notes in Mathematics, vol. 1052. Springer, Berlin (1984)","DOI":"10.1007\/BFb0071540"},{"key":"1071_CR12","volume-title":"Higher Transcendental Function, vol. 1","author":"A Erd\u00e9lyi","year":"1953","unstructured":"Erd\u00e9lyi, A., et al.: Higher Transcendental Function, vol. 1. McGraw Hill Book Co., Inc., New York (1953)"},{"key":"1071_CR13","volume-title":"q-Hypergeometric Functions and Applications","author":"M Exton","year":"1983","unstructured":"Exton, M.: q-Hypergeometric Functions and Applications. Ellis Horwood series in mathematics and its applications, Chichester (1983)"},{"key":"1071_CR14","doi-asserted-by":"crossref","unstructured":"Farin, G.: Curves and Surfaces for Computer Aided Geometric Design: a Practical Guide. Ac Press (1993)","DOI":"10.1016\/B978-0-12-249052-1.50005-2"},{"key":"1071_CR15","doi-asserted-by":"crossref","unstructured":"Gasper, G., Rahman, M.: Basic Hypergeometric Series. In: Encyclopedia Mathematics and its Applications, vol. 96. Cambridge University Press (2004)","DOI":"10.1017\/CBO9780511526251"},{"key":"1071_CR16","first-page":"157","volume-title":"Pad\u00e9 approximation to the logarithmic derivative of the Gauss hypergeometric function, Analytic number theory","author":"M Hata","year":"2002","unstructured":"Hata, M., Huttner, M.: Pad\u00e9 approximation to the logarithmic derivative of the Gauss hypergeometric function, Analytic number theory, pp 157\u2013172. Springer, Boston (2002)"},{"key":"1071_CR17","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/BF02420446","volume":"21","author":"C Hermite","year":"1893","unstructured":"Hermite, C.: Sur la g\u00e9n\u00e9ralisation des fractions continues alg\u00e9briques. Annali Math. Pura Appl. 21, 289\u2013308 (1893)","journal-title":"Annali Math. Pura Appl."},{"key":"1071_CR18","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/BF01442748","volume":"22","author":"A Hurwitz","year":"1883","unstructured":"Hurwitz, A.: Uber arithmetische Eigenschaften gewisser transcendenter Funktionen. Math. Ann. 22, 211\u2013229 (1883)","journal-title":"Math. Ann."},{"key":"1071_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0071-7","volume-title":"Quantum calculus, Universitext series, IX","author":"V Kac","year":"2002","unstructured":"Kac, V., Cheung, P.: Quantum calculus, Universitext series, IX. Springer, Berlin (2002)"},{"key":"1071_CR20","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s00365-010-9111-x","volume":"33","author":"T Matala-aho","year":"2011","unstructured":"Matala-aho, T.: Type II Hermite-Pad\u00e9 approximations of generalized hypergeometric series. Constr. Approx. 33, 289\u2013312 (2011)","journal-title":"Constr. Approx."},{"key":"1071_CR21","unstructured":"Mazure, M.-L., Laurent, P.-J.: Affine and non-affine blossoms. In: Conte, R., Demichelis, V., Fontanelle, F., Galligani, I. (eds.) Torino Workshop on Computational Geometry, pp 201\u2013230. World Scientific Pub., Singapore (1993)"},{"key":"1071_CR22","unstructured":"Mazure, M.-L.: Blossoming and CAGD algorithms. In: Shape Preserving Representations for Computer-Aided Design, pp 99\u2013117. Nova Science Pub. (1999)"},{"key":"1071_CR23","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s003659900096","volume":"15","author":"M-L Mazure","year":"1999","unstructured":"Mazure, M.-L.: Blossoming: a geometrical approach. Constr. Approx. 15, 33\u201368 (1999)","journal-title":"Constr. Approx."},{"key":"1071_CR24","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1007\/s10543-013-0432-6","volume":"53","author":"M-L Mazure","year":"2013","unstructured":"Mazure, M.-L.: Extended Chebyshev spaces in rationality. BIT Num. Math. 53, 1013\u20131045 (2013)","journal-title":"BIT Num. Math."},{"key":"1071_CR25","doi-asserted-by":"publisher","first-page":"1977","DOI":"10.1142\/S1793042111004964","volume":"7","author":"V Meril\u00e4","year":"2011","unstructured":"Meril\u00e4, V.: A nonvanishing lemma for certain Pad\u00e9 approximations of the second kind. Intern. J. Number Theory 7, 1977\u20131997 (2011)","journal-title":"Intern. J. Number Theory"},{"issue":"1995","key":"1071_CR26","first-page":"189","volume":"83","author":"YV Nesterenko","year":"1994","unstructured":"Nesterenko, Y.V.: Hermite-Pad\u00e9 approximants of generalized hypergeometric functions. Russ. Acad. Sci. Sb. Math. 83(1995), 189\u2013219 (1994)","journal-title":"Russ. Acad. Sci. Sb. Math."},{"key":"1071_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0377-0427(02)00733-1","volume":"151","author":"H Oru\u00e7","year":"2003","unstructured":"Oru\u00e7, H., Phillips, G.M.: q-Bernstein polynomials and B\u00e9zier curves. J. Comp. Appl. Math. 151, 1\u201312 (2003)","journal-title":"J. Comp. Appl. Math."},{"key":"1071_CR28","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/0167-8396(93)90036-3","volume":"10","author":"H Pottmann","year":"1993","unstructured":"Pottmann, H.: The geometry of Tchebycheffian splines. Comput. Aided Geom. Design 10, 181\u2013210 (1993)","journal-title":"Comput. Aided Geom. Design"},{"key":"1071_CR29","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/0167-8396(89)90032-0","volume":"6","author":"L Ramshaw","year":"1989","unstructured":"Ramshaw, L.: Blossoms are polar forms. Comput. Aided Geom. Design 6, 323\u2013358 (1989)","journal-title":"Comput. Aided Geom. Design"},{"key":"1071_CR30","unstructured":"Seigel, C.L.: \u00dcber einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss., KL, 1 (1929)"},{"key":"1071_CR31","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.jat.2011.09.006","volume":"164","author":"P Simeonov","year":"2012","unstructured":"Simeonov, P., Zafiris, V., Goldman, R.: q-Blossoming: a new approach to algorithms and identities for q-Bernstein bases and q-B\u00e9zier curves. J. Approx. Theory 164, 77\u2013104 (2012)","journal-title":"J. Approx. Theory"},{"key":"1071_CR32","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/BF01463871","volume":"268","author":"T Stihl","year":"1984","unstructured":"Stihl, T.: Arithmetische Eigenschaften spezieller Heinescher Reihen. Math. Ann. 268, 21\u201341 (1984)","journal-title":"Math. Ann."},{"key":"1071_CR33","unstructured":"Thue, A.: Bemerkungen \u00fcber gewisse n\u00e4herungsbr\u00fcche algebraischer Zahlen. Kra. Vidensk. Selsk. Skrifter. I. Mat. Nat. K. 3 (1908)"},{"key":"1071_CR34","unstructured":"Thue, A.: \u00dcber rationale ann\u00e4herungswerte der reellen w\u00fcrzel der ganzen Funktion dritten Grades x3 \u2212 ax \u2212 b. Kra. Vidensk. Selsk. Skrifter. I. Mat. Nat. M. 6 (1908)"},{"key":"1071_CR35","first-page":"61","volume":"2","author":"W Van Assche","year":"2006","unstructured":"Van Assche, W.: Pad\u00e9 and Hermite-Pad\u00e9 approximation and orthogonality. Surv. Approxim. Theory 2, 61\u201391 (2006)","journal-title":"Surv. Approxim. Theory"},{"key":"1071_CR36","unstructured":"Waldschmidt, M.: Introduction to Diophantine methods: irrationality and transcendence, https:\/\/webusers.imj-prg.fr\/michel.waldschmidt\/coursHCMUNS2007.html"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-021-01071-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-021-01071-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-021-01071-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,25]],"date-time":"2022-12-25T09:57:33Z","timestamp":1671962253000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-021-01071-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,23]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["1071"],"URL":"https:\/\/doi.org\/10.1007\/s11075-021-01071-3","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2021,4,23]]},"assertion":[{"value":"6 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}